1,721,363 research outputs found
Modeling churn using customer lifetime value
Full text linkThe definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution is to redefine the notion of customer loyalty by considering it from a customer-centric viewpoint instead of a product-centric one. We hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer’s activity. Hence, a churner is defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease is used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classifiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures for prediction need to be revised and a more profit oriented focus may be desirable.<br/
A modified Pareto/NBD approach for predicting customer lifetime value
Full text linkValuing customers is a central issue for any commercial activity. The customer lifetime value (CLV) is the discounted value of the future profits that this customer yields to the company. In order to compute the CLV, one needs to predict the future number of transactions a customer will make and the profit of these transactions. With the Pareto/NBD model, the future number of transactions of a customer can be predicted, and the CLV is then computed as a discounted product between this number and the expected profit per transaction. Usually, the number of transactions and the future profits per transaction are estimated separately. This study proposes an alternative. We show that the dependence between the number of transactions and their profitability can be used to increase the accuracy of the prediction of the CLV. This is illustrated with a new empirical case from the retail banking sector.<br/
Robust discriminant analysis.
Full text linkRobuuste discriminant analyse Discriminant analyse, en de bijhorende classificatieregels, wordt vaak g ebruikt in de praktijk. Denk bijvoorbeeld aan de marketing afdeling van een bank die tracht beleggingsfondsen te verkopen aan nieuwe klanten. Ve rmits men uiteraard niet onnodig nieuwe klanten wenst lastig te vallen, wil men ervoor zorgen dat de reclame alleen aan mogelijk geïnteresseerde n gegeven wordt. Discriminant analyse kan hier helpen, maar er moet reke ning mee gehouden worden dat de gegevensbank waarover de bank beschikt e rg groot kan zijn, en dat deze vele atypische observaties kan bevatten, ook wel uitschieters genaamd. In discrimin antanalyse tracht men een regel op te stellen die toelaat o m multivariate observaties aan verschillende groepen toe te wijzen. Deze regel wordt geconstrueerd op basis van een oefensteekproef, wat een ver zameling observaties is waarvan men reeds weet tot welke groep ze behore n. Als voorbeeld kan als oefensteekproef een verzameling cliënten bescho uwd worden. Een deel hiervan zijn mensen die reeds beleggingsfondsen heb ben en een ander deel niet. Voor al deze cliënten worden enkele relevant e karakteristieken gemeten, zoals het spaargeld, het gezinsinkomen, info rmatie over lopende leningen, het aantal kinderen, enz. Gebruikmakende v an deze informatie kan men dan een discriminant regel opstellen, die toe gepast kan worden op nieuwe cliënten waarvan men enkel de karakteristiek en kent, doch die niet in de oefensteekproef zaten. Deze cliënten kunnen dan toegekend worden aan één van de groepen. Enkel de nieuwe cliën ten die toegekend worden aan de groep van mensen geïnteresseerd in beleg gingsfondsen, zullen de reclame ontvangen. Vele andere toepassingen van discriminant analyse kunnen uiteraard gevonden worden in economie, biolo gie, geneeskunde, enz. De klassieke discriminant regels kunnen echter erg sterk beïnvloed worde n door aanwezigheid van enkele uitschieters in de oefensteekproef, waard oor de resultaten onbetrouwbaar kunnen worden. Daarom is er nood aan rob uuste alternatieven die zich stabieler gedragen in aanwezigheid van uits chieters in de data. In de literatuur werden reeds resultaten voor robuu ste discriminant analyse gegeven, doch dit was meestal beperkt tot linea ire discriminant analyse en in het geval van slechts twee groepen. In di t proefschrift worden ook robuuste niet-lineaire discriminant regels bes tudeerd, zoals kwadratische en logistische regels. Tevens wordt in dit p roefschrift een uitbreiding naar discriminant analyse voor meerdere groe pen voorzien. Het kan bijvoorbeeld zeer interessant zijn om groepen van beleggers te onderscheiden, afhankelijk van de karakteristieken van de p ersonen in die verschillende groepen. In dit proefschrift werden nieuwe discriminant procedures ontwikkeld, di e zich robuust gedragen in aanwezigheid van uitschieters en een zo klein mogelijke kans op foutieve classificatie geven. Statistische eigenschap pen werden afgeleid voor de verscheidene methodes en voorgesteld in de v erschillende artikels die reeds gepubliceerd werden of reeds ingestuurd werden voor publicatie. Ze situeren zich allemaal in het domein van robu uste statistiek. Naast robuuste discriminant analyse, werd o ok aandacht geschonken aan robuuste tijdreeksenanalyse.status: Publishe
Robust and sparse estimation in high-dimensions.
No full textClassical parametric statistics commonly makes assumptions about the data (e.g. normal distribution). These assumptions are often very strong and hardly fulfilled in practice. Another problem with real data is the occurrence of gross errors (e.g typos) or the presence of subpopulations (a small number of observations that behave totally different than the rest). Such atypical observations are called contaminated observations. To be robust against contamination, robust statistics focuses on fitting the desired model to the main part of the data, while not taking suspicious observations too much into account.
The usual assumption in robust statistics is that the main part of the observed data follows a specified model distribution (like in classical parametric statistics), but that a small part of the observed data comes from an arbitrary, unspecified distribution. This assumption refers to rowwise contamination. The name comes from representing observed data in a matrix where the different rows represent the different observations, and the columns the observed variables. Rowwise robust methods then detect either a whole observation (row) as outlying or not. In contrast, cellwise robust methods consider single cells of the matrix as outlying. Cellwise contamination can occur if the different variables are measured separately or obtained from different sources. In such scenarios, it seems more appropriate to allow that some variables of one observation can be treated as outliers, while other variables of the same observations are labeled as clean. This is especially interesting if the number of observations is low and the number of variables large. Treating a full observation as an outlier, even though only one cell is contaminated, would then lead to a large loss of information. Furthermore, if the amount of cellwise contamination is so high that more than half of the observations are affected, most rowwise robust methods do not give reliable results anymore.
In recent years, the number of data sets containing a large number of variables is increasing rapidly. In practice, collection of observations is rather expensive. Therefore, more and more data sets contain (many) more variables than observations. Such high-dimensional data sets often cannot be analyzed with classical statistics. Least squares regression, for example, cannot be carried out because the problem is ill-posed.
In this thesis, we study robustness properties of high-dimensional estimators in Chapter 1. A new robust, high-dimensional regression estimator is introduced and studied in Chapter 2. In Chapter 3, we study the robustness of a recently introduced covariance estimator. The last chapters are dedicated to cellwise robustness: A regression estimator for cellwise contamination is introduced in Chapter 4. In Chapter 5, we develop a cellwise robust scatter estimator which is especially useful for high-dimensional analysis. This estimator, we compare to other high-dimensional approaches in Chapter 6.status: Publishe
Essays over tijdsvariërende relaties in multi-landen macro-economische tijdreeksen.
No full textThe main goal of empirical macroeconomics is to understand the relationships between macroeconomic variables, such as the gross domestic product (GDP), inflation and interest rates. This allows for better macroeconomic predictions and helps macroeconomic policy makers to set a sound fiscal and monetary policy. For example, understanding the effect of the short term interest rate on inflation is essential for a central bank, which is responsible for price stability. Also, good GDP predictions allow governments to anticipate the future evolution of the economic activity by taking stabilizing actions in advance.
Empirical macroeconomic analysis usually starts from a time series dataset in which the variables of interest are observed for subsequent time periods, typically quarterly. Such datasets thus consist of historical data, where the observations are realizations of how the economy has behaved in the past, and which makes it difficult to derive causal relationships between the variables. In contrast, note that in experimental data, used in for instance pharmaceutical studies, cause and effect can be clearly distinguished by exogenously manipulating a variable, for example the intake of a certain drug, and then observing the consequences on another variable, for example the patient’s health. Still, also information on the linkages between macroeconomic variables can be obtained. First, instead of true causality, macroeconomists often study the incremental predictive power between variables instead, which is called ‘Granger causality’. A variable is said to Granger cause another variable if it improves the prediction of the other variable. Second, macroeconomists often make additional ‘identification assumptions’ on the causality between the variables, which allows them to extract exogenous shocks. One popular identification assumption is the ‘recursive ordering scheme’, in which the ordering of the variables determines how rapidly the different variables can react to exogenous shocks in the other variables. For example, it is typically assumed that inflation and GDP are relatively sluggish variables, such that they do not immediately react to an interest rate shock.
In order to extract patterns from the macroeconomic dataset, statistical models are used. In this thesis, we mainly use the Vector Autoregression (VAR) model, which is the workhorse in empirical macroeconomics to study linear relationships between multiple time series. Unlike more structural economic models, VAR models are fully data-driven and require no ex-ante expert knowledge on the dependencies between the variables. In the VAR model, each variable depends on both the past values of the variables in the model and a shock. The vector autoregression coefficients thus represent the effects of past values of the variables on the current value of each variable. While the standard VAR model assumes that these coefficients stay the same over time, this thesis focuses on modeling changing macroeconomic relationships. First, Time Varying Parameter Vector Autoregression (TVP VAR) models allow the vector autoregression coefficients to evolve smoothly over time. For example, the effect of an interest rate shock on inflation is found to be different in the 1970s compared to the period afterwards. Second, frequency domain techniques describe the time series as a weighted sum of sinusoidal components with different frequencies, for instance slowly fluctuating and quickly fluctuation. Interestingly, the relationships between the variables can differ across these different frequency components. Third, for a panel dataset in which the variables are observed both for subsequent time periods and different countries, also the cross-country variation in the coefficients can be analyzed.
This thesis contains essays on the empirical relationship between macroeconomic time series, often in a multi-country setting. While the standard VAR model is used in Chapter 2, the time variation in the coefficients is studied in Chapters 3 and 5, the frequency domain analysis is performed in Chapter 1 and the cross-country variation is analyzed in Chapter 4.
The first chapter studies the predictive power of domestic stock prices for the future domestic economic activity in the frequency domain. We develop a multi-country test for Granger causality for each of the frequency components. Using 1991Q1-2010Q2 quarterly data for the G-7 countries, we report that the slowly fluctuating components of stock prices have large incremental predictive power for the future GDP, while this is not the case for the quickly fluctuating components.
The second chapter analyzes impulse response functions of vector autoregression models for variables that are linearly transformed. The impulse response function of a vector autoregression model is an often used tool in empirical macroeconomics to analyze the response of the variables in the model to different types of shocks. For many empirical applications, it is of interest to know how the impulse response functions would change if one or more variables in the VAR model are replaced by a linear transformation of the original variables. One example of such a transformation is the replacement of a nominal growth rate variable in a VAR model that also includes inflation by its corresponding real growth rate variable, which is the difference between the nominal growth rate variable and inflation. We show that the new impulse response is equal to the linear transformation of the original impulse response if and only if the new shock is equal to the linear transformation of the original shock. Sufficient conditions for this relationship between impulse responses are derived for the setting where the same type of shock is studied in the linearly transformed and original model. In particular, we consider shocks in one error term only, orthogonalized shocks and generalized shocks.
The third chapter compares Bayesian estimators with different prior choices for the amount of time variation in the coefficients of time varying parameter vector autoregression models using Monte Carlo simulations. In Bayesian statistics, the posterior estimate of the parameters in the model is a combination of, on the one hand, the prior assumption on the distribution of these parameters and, on the other hand, the information contained in the data. When the sample size is very large, the prior specification is not that important as it is swamped by the large amount of information in the data. However, for typical macroeconomic time series, the prior is very important. Since the commonly used prior only allows for a tiny amount of time variation, less restrictive priors are proposed. Additional empirical evidence on the time varying response of inflation to an interest rate shock is then provided for USA: while a major and statistically significant ‘price puzzle’ is detected for the period 1972-1979, the estimated response of inflation to an interest rate shock is negative for most other time periods.
The fourth chapter investigates empirically how the impact of a residential house price shock on household credit and GDP is influenced by the degree of the mortgage market flexibility. Countries with a flexible mortgage market, such as United States and United Kingdom, are characterized by a high loan to value ratio, low transaction costs of mortgage refinancing and easy access to second mortgages and home equity loans. Countries with an inflexible mortgage market, such as France and Italy, are characterized by the opposite. We hypothesize a stronger effect of house price shocks for the former countries because the financial accelerator mechanism for existing home owners is expected to be stronger and because the effect of higher house prices on the required amount of savings of future first time house buyers is expected to be smaller. A panel vector autoregression model is estimated separately for a group of eight countries with a flexible mortgage market and for a group of eight countries with an inflexible mortgage market. While both household credit and GDP increase after a positive house price shock for both groups of countries, we do not find empirical evidence that these responses are stronger for countries with a flexible mortgage market.
The fifth chapter investigates the determinants of sovereign credit ratings, which are ordinal measures of the creditworthiness of a sovereign government assigned by a rating agency. We quantify for the three major credit rating agencies how the importance of the different sovereign credit rating determinants changed after the start of the European debt crisis in 2009. For this end, we estimate a multi-year ordered probit model, using a sample of 90 countries for the years 2002-2015. Our model allows for time variation in the importance of the different determinants and it takes into account the ordinal nature of the credit rating. We provide empirical evidence that the credit rating agencies changed their sovereign credit rating assessment after the start of the European debt crisis in 2009. The financial balance, the economic development and the external debt became substantially more important after 2009 and the effect of Eurozone membership switched from positive to negative. In addition, GDP growth gained a lot of importance for highly indebted sovereigns and government debt became much more important for countries with a low GDP growth rate.
In the epilogue chapter, I give my personal view on the way statistical inference should be used in business and economic applications. In particular, I call for more focus on the evaluation of ‘economic importance’, i.e. the estimated magnitude of an effect together with its estimation error, and for less focus on the often less relevant and frequently misunderstood concept of ‘statistical significance’, which only informs on the existence of the effect.status: Publishe
Sparse estimation of high-dimensional time series models.
No full textNowadays, a large amount of data is available in nearly every area of science and business. Information is typically collected in data sets where the different variables are contained in the columns of the data set and the measurements on each variable are contained in the rows. Our interest mainly lies in settings where these measurements are collected over time. Such data sets are said to contain time series in their columns. A time series should be treated differently from a regular variable to account for the time-dependency of its measurements.
Moreover, given today's data abundance, our interest lies in high-dimensional data sets, as opposed to low-dimensional data sets. High-dimensional time series data sets contain many short time series: a large number of time series (columns) is available relative to the number of time points (rows), hence, these data sets are `fat'. Low-dimensional time series data sets, in contrast, contain few long time series: a large number of time points (rows) is available relative to the number of time series (columns), hence, these data sets are `thin'. High-dimensional time series data sets are commonplace in today's business practice since many firms collect information on a large number of variables, but discard data that are older than a few years.
The problem, however, is that traditional estimators are well suited for low-dimensional data sets, but not for high-dimensional data sets. On the one hand, these estimators suffer from very low estimation precision if the number of measurements (rows) is close to the number of variables (columns) in the data set. On the other hand, traditional estimators are not even computable if the number of measurements (rows) in the data set is larger than the number of variables (columns). Hence, there is a need for new estimation methods especially designed for these high-dimensional data sets.
In this thesis, we develop sparse estimation methods for high-dimensional data. Despite the data abundance, we do not expect each variable of these data sets to be equally informative. Sparse estimation methods rely on a simplicity assumption: we assume that only a relative small number of variables in our data set plays an important role. As such, sparse estimators retain the informative variables and remove the non-informative ones. This highly facilitates interpretation.
We develop sparse estimators for high-dimensional time series models in Chapters 1 to 4, and for Canonical Correlation Analysis (CCA) in Chapters 5 and 6. CCA is a multivariate statistical method that describes the associations between two data sets. Our interest lies in settings where both data sets are high-dimensional. Throughout the thesis, the usefulness and relevance of the sparse estimators are discussed for a wide variety of application domains, ranging from marketing (Chapter 1), and economics (Chapter 3, 4), to biometrics (Chapter 2, 5, 6).status: Publishe
Essays on paid, owned and earned media in multimedia contexts.
No full textThe three essays in this dissertation deal with un(der)explored challenges for marketing academics and practitioners concerning varying multimedia contexts, including (yet not limited to) self-selection issues, synergies, mediation effects and consistency issues.
According to Corcoran (2009), marketing media can be classified into three categories. First, paid media are third-party channels that firms/brands pay for to leverage. This category mainly consists of advertising, but also entails, e.g., paid search, display ads, pay per click and sponsorships. Second, owned media are channels that the firm/brand creates and controls, with the firm/brand’s website or brochures as the most common examples. Last, earned media are channels through which consumers and the press share a firm/brand’s content, and speak about brands via word of mouth. These media differ from paid and owned media in that they are entirely initialized by consumers, and thus have to be “earned” by firms/brands. Examples include Facebook comments, Twitter replies, blogs, forums and review websites.
Figure 1 shows how the three essays presented in this dissertation fit into the spectrum provided by the POE (paid-owned-earned) media classification. Essay 1, which has been published in the International Journal of Research in Marketing in December 2014, deals solely with paid media and is titled “Billboard and cinema advertising: Missed opportunity or spoiled arms?”. In this essay, we perform a meta-analytic study on the short- and long-run effectiveness of two smaller, less studied advertising media, i.e. billboards and cinema, for 250+ mature CPG brands. While quantifying the effectiveness of these media using advertising elasticities, we correct for the potential bias in these estimates due to the self-section of brands in their media usage. We do not
only do this for the two small media, but also for four larger, more traditional advertising media, i.e. TV, radio, newspapers and magazines. Furthermore, we look into the possibility of synergy effects between these larger media on the one hand and the small media on the other hand. The results of our analysis show that after correcting for self-selection, which turns out to be highly relevant for drawing appropriate conclusions on media effectiveness for the general population of CPG brands, only TV advertising significantly impacts both sales and market share in the long run. Magazine advertising generally leads to primary-market expansion, but does not induce competitive gain, meaning that it tends to improve sales but not market share. The two small media of interest, i.e. billboard and cinema, are spoiled arms for most mature CPG brands, at least from a sales-response (and market-share) point of view. Although this result is a conservative one for cinema advertising, two remarks need to be made on billboard advertising. First, although billboard advertising is ineffective for an average CPG brand, its long-run effect among the subset of users of this medium is significant. Hence, the (small) subset of brands that makes use of this medium appears well-informed (on average) that this medium works for them. Second, a significant long-run synergy effect exists between radio and billboard advertising, indicating that billboard advertising can be useful if it is used together with radio media. However, brands fail to capitalize on this opportunity as the simultaneous use of both media is rare in our data set.
In Essay 2, titled “Online user-generated content: The (in)consistency among hotel-rating websites”, our research setting switches from paid to earned media. In this paper, we address the issue that the vast expansion of the Internet has created an extensively large set of platforms on which consumers can share their opinions with each other, and that users of these platforms might get lost in the abundance of information at their disposition. In order to provide consumers with advice on whether they should consult multiple rating websites (i.c. hotel rating websites) to obtain a reliable indicator of quality as perceived by their peers or whether consulting one of the more prominent websites suffices, we perform a consistency analysis on 665 Parisian hotels rated on four of the most popular customer review websites – i.e. TripAdvisor, Booking.com, Expedia and HolidayCheck. The according results provide substantial evidence of the high level of consistency among three of these four platforms. It is, however, important to note that the consistency here lies in corresponding rating behavior and patterns, rather than actual rating scores. Consumers are consequently advised to rely on TripAdvisor’s, Booking.com’s or Expedia’s ratings, although the mean of these scores would improve the reliability performance even further. HolidayCheck, in contrast, shows a relatively low level of consistency with the three other websites. As the drivers behind this discrepancy are unclear, further research on this matter might be called for.
While Essays 1 and 2 revolve around multimedia research questions within one media category (i.e., paid or earned media), Essay 3 focuses on a context including two types of media, being paid and owned media. This essay is titled “Media effectiveness in the non-profit entertainment industry”. The objective of this paper is (i) to put in contrast the sales-driving roles of traditional advertising and informational websites, and (ii) to test for a potential mediating or moderating effect of the former media on the latter. We situate this research in a non-profit setting, where marketing accountability is even more pressing than in for-profit industries. Relying on the case of Technopolis, a Belgian science-themed entertainment park, we are able to show how the owned medium, i.e. the informational website, is a much more important attendance driver (and likely at a much lower cost) than both print and radio advertising. As such, our results support the industry claim that owned online media can well become a cost-effective complement for cash-constrained non-profit organizations. Further, our analysis provides no empirical evidence of any mediating or moderating role of print or radio advertising on the consumers’ activity on the informational website. A better alignment of the on- and offline media might thus further improve these media’s effectiveness.
In conclusion, besides the academic relevancy of the provided research, the three essays in this dissertation also provide valuable insights for both marketing managers and consumers. First, the examination of advertising-channel effectiveness in the CPG market gives rise to guidelines on budget allocation for start-ups, while it might urge established brands to reevaluate and possibly rethink their current advertising strategy. Also, it brings to light the opportunity of synergistic effects between radio and billboard advertising. Second, our results on website effectiveness and the lack of evidence for its mediating and moderating effect with more traditional media, shows the high potential effect of online media in the marketing strategy and hopefully might serve as a driver for marketing managers to strengthen the alignment between online and offline media. Last, our third paper shows that consumers can rely on most of the major hotel rating websites and that they should accordingly not have to go through an extensive research process across multiple websites to obtain an adequate representation of quality as perceived by their peers.
The three essays in this dissertation also open up new paths for future research on POE media. For example, given that we could not find any empirical evidence of a general effectiveness of cinema and billboard advertising on sales and market share, it would be interesting to study their effect on mindset metrics, such as brand recognition or liking. Also, it would be interesting to study the exceptional cases in which these small media do tend to be effective, in order to depict common brand or campaign characteristics that are crucial for the success of billboard or cinema advertising. Furthermore, with our results on media effectiveness in the non-profit industry, which deviate from prior results obtained in the for-profit industry, we hope to stimulate further research on this topic. Last, further research is warranted on the consistency subject of online rating websites. For example, it might be interesting to determine the causes of the differences in rating values across different websites, not only in the hotel industry but also beyond.status: Publishe
Predictive modelling: variable selection and classification efficiencies.
Full text linkOp de dag van vandaag worden er enorm veel gegevens gedurende studies over economische, medische, biochemische, en vele andere fenomenen. Voorbeelden van zulke datasets zijn bijvoorbeeld gegevens over klanten voor het bepalen van hun kredietrisico (voor banken), hun risico op ongevallen (voor verzekeringsmaatschappijen). Andere voorbeelden zijn onder andere epidemiologische studies, en studies naar genetische relevantie. Ook gebeurt het steeds meer dat deze datasets veel verschillende variabelen bevatten, waarvan de meeste waarschijnlijk niets te maken hebben met het onderzochte fenomeen. Daarom zijn er technieken nodig die een groep van variabelen kunnen selecteren, liefst zo klein mogelijk, of een zo eenvoudig mogelijk model, dat toch een goed model is voor het onderzochte fenomeen. Daartoe zijn er al verschillende modelselectiecriteria ontwikkeld, zoals Akaikes Informatiecriterium (AIC), het Bayesiaans of Schwarz Informatiecriterium (BIC/SIC), het Cp criterium van Mallows, and meer recent, het Focussed Informatiecriterium (FIC). De eerste drie criteria in deze lijst laten toe van één bepaald model te kiezen om het onderzochte fenomeen te verklaren, waarvoor dit model ook gebruikt zal worden. Hoewel deze criteria doorgaans een model kiezen dat behoorlijk werkt, is het niet noodzakelijk optimaal voor het uiteindelijke doel, bijvoorbeeld om voorspellingen te maken. Het laatste criterium echter, het FIC, heeft dit probleem niet en zal een model kiezen dat op maat gemaakt is voor wat de onderzoeker voor ogen heeft, waardoor het gekozen model mogelijk beter presteert voor dat bepaald doel. In het eerste hoofdstuk van deze thesis bekijken we het probleem van doelgerichte variabelenselectie in het logistisch regressiemodel. Hier zal het FIC verschillende modellen kiezen naargelang de observatie waarover de voorspelling wordt gemaakt, wat tot nauwkeurigere voorspellingen zal leiden. Dit is vooral interessant voor zakenmanagers als ze willen voorspellen dat een bepaalde investering zal renderen of niet. Een andere toepassing bevindt zich in de medische wereld, waar het van levensbelang is dat patiënten een correcte diagnose krijgen dat ze al dan niet een bepaalde ziekte hebben. De gewone FIC schat de gemiddelde kwadratische fout van de schatter van de parameter die ons interesseert, waarbij we hier de score van de te voorspellen observatie kiezen. In dit hoofdstuk hebben we een algemenere versie van FIC voorgesteld met een algemene risicomaat gebaseerd op de Lp-fout. De hoofdverwezenlijking hier is het opstellen van een FIC waarbij de kans op een foute voorspelling als risicomaat wordt gebruikt, vermits we een ja/nee uitkomst willen voorspellen. De voordelen van het gebruik van een informatiecriterium dat zijn model kiest afhankelijk van de te voorspellen observatie werden aangetoond aan de hand van een simulatiestudie en een toepassing op een medische studie. In het tweede hoofdstuk van de thesis passen we het FIC toe op het kiezen van de autoregressie (AR) orde van een stationaire tijdreeks. Autoregressieve tijdreeksen worden in economie vaak gebruikt om een fenomeen zoals wisselkoersen of werkloosheidsgraad over de tijd te modelleren. Deze modellen worden dan gebruikt om dit fenomeen te voorspellen voor de (nabije) toekomst. Deze voorspellingen moeten zo nauwkeurig mogelijk zijn, dit in het bijzonder voor macro-economische fenomenen, zodanig dat de beleidsmensen hierop kunnen vertrouwen voor het nemen van goede beslissingen. Het focussed informatiecriterium was oorspronkelijk gedefinieerd voor een vaste groep van modellen, waarbij het grootste beschouwd model niet verandert als er observaties bijkomen. In dit hoofdstuk ontwikkelden we het FIC verder zodanig dat dit criterium kan gebruikt worden in de situatie waar de maximale AR orde van de beschouwde modellen naar oneindig gaat als de lengte van de tijdreeks stijgt. We hebben dit resultaat voor twee redenen nodig. Eerst en vooral is het aantal mogelijke variabelen theoretisch oneindig als we werken met autoregressieve modellen. Een belangrijkere reden is dat we de asymptotische efficiëntie van FIC wensen te onderzoeken, en dit willen vergelijken met AIC voor modelorde selectie. We hebben dit onderzocht aan de hand van een uitgebreide simulatiestudie, waarbij we zowel het geval van twee tijdreeksen hebben onderzocht, waar AIC asymptotisch de meest nauwkeurige modellen selecteert, als het geval van één enkele tijdreeks, waar AIC deze eigenschap ook heeft. Gedurende deze studie hebben we gemerkt dat de prestaties van de modellen geselecteerd door FIC zeer dicht liggen bij de prestaties van de modellen geselecteerd door AIC en dat dit verschil kleiner wordt als de lengte van de tijreeks stijgt. Het FIC kan ook gebruikt worden om het beste model te kiezen voor het schatten van de impulsresponsfunctie voor een bepaalde lag. In dit geval zien we dat de prestaties van FIC en AIC sterk variëren naargelang de parameters van het echte, datagenererend model veranderen, en dat geen van beide uniform beter is dan het andere. Ook hebben we aangetoond dat FIC eenvoudig kan worden toegepast voor moeilijkere variabelenselectie problemen voor tijdreeksen, zoals het tegelijkertijd selecteren van de regressievariabelen en de AR orde van de residuen. De criteria in de voorgaande paragrafen hebben één groot nadeel. Omdat ze gebaseerd zijn op de likelihood van de gegevens, kunnen ze niet gebruikt worden als het aantal variabelen groter is dan het aantal observaties. Daarom hebben we eerst een alternatief voor maximum likelihood schatters nodig, zodanig dat we de parameters van het model kunnen schatten. De Support Vector Machine (SVM) laat binaire classificatie toe als het aantal variabelen (veel) groter is dan het aantal observaties. Het is echter nog altijd aan te raden om de dimensie van de ruimte van de observaties te verkleinen, omdat dit de voorspellende prestaties van het model kan vergroten. Er zijn reeds verschillende technieken om variabelenselectie te doen voor de SVM, maar weinigen ervan werken met informatiecriteria. Technieken die toch op criteria zijn gebaseerd zijn bijvoorbeeld deze gebaseerd op de crossvalidatie voorspellingsfout, of het Kernel Regularisatie Informatiecriterium (KRIC). In het derde hoofdstuk van deze thesis hebben we twee nieuwe informatiecriteria ontwikkeld (SVMICa en SVMICb) die voor variabelenselectie in SVMs kunnen worden gebruikt. Deze nieuwe criteria hebben als voordeel dat ze niet zo veel extra berekeningen vragen als de bestaande criteria, en dat ze dus sneller te berekenen zijn. Ook hebben we het SVMICa gekoppeld aan het KRIC, als een benadering onder bepaalde voorwaarden. Daarna hebben we een uitgebreide simulatiestudie uitgevoerd waarin we de eigenschappen van SVMICa/b hebben onderzocht, en we hebben gezien dat de modellen geselecteerd door deze criteria degelijke voorspellende eigenschappen hebben. Daarenboven blijkt SVMICb de asymptotische consistentie eigenschap te hebben. Deze goede eigenschappen werden ook bevestigd gedurende een test op een aantal echte datasets. Een andere kwestie die toch zeer belangrijk is in het voorspellend modelleren is, is de vraag hoe efficiënt een schattingsmethode voor een bepaald model is. Doorgaans moet je een keuze maken tussen efficiëntie van de methode, en hoe algemeen toepasbaar of hoe robuust die methode is. Het onderzoeken van deze efficiënties laat ons dus toe te zien welke prijs (in termen van efficiëntie) je betaalt voor het gebruik van algemenere en/of robuustere schattingsmethoden. In het laatste hoofdstuk van de thesis hebben we de classificatie-efficiëntie van een groep beslissingsregels, gekend als de Convex Risico Minimalisatie (CRM) regels, onderzocht. Deze methoden zijn een zeer flexibele groep van schattings-technieken voor het schatten van de beslissingfunctie in binaire classificatie, in de zin dat deze eenvoudig kunnen aangewend worden voor niet-lineaire problemen. We hebben de CRM technieken vergeleken met de bekende lineaire discriminatieregel van Fisher, dit in het geval van twee normaalverdeelde populaties met gelijke variantie. In deze situatie weten we dat de regel van Fisher efficiënt is. Om die classificatie-efficiënties te bereken, maken we gebruik van invloedsfuncties. Eerst en vooral hebben we een theoretische uitdrukking gevonden voor deze invloedsfuncties voor Fisher-consistente CRM regels, regels die de laagst mogelijke voorspellingsfout hebben. Ook hebben we voldoende condities opgesteld waarvoor zulke Convex Risico Minimalisatie methodes Fisher-consistent zijn. Daarna hebben we een gedetailleerde analyse gedaan voor een aantal CRM methodes, en we hebben gevonden dat voor redelijk gebalanceerde, slecht scheidbare populaties, de CRM methodes redelijk efficiënt zijn, met efficiëntie boven de 50%, terwijl ze toch veel flexibeler zijn dan de efficiënte regel van Fisher.status: Publishe
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