1,721,037 research outputs found
Universality of free homogeneous sums in every dimension
No full textWe prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type Un(S), where Un(x) is the n-th Chebyshev polynomial and S is a standard semicircular element on a fixed W*-probability space. As a consequence, we deduce that homogeneous sums based on random variables of this type are universal with respect to both semicircular and free Poisson approximations. Our results are stated in a general multidimensional setting and can be seen as a genuine extension of some recent findings by Deya and Nourdin; our techniques are based on the combination of the free Lindeberg method and the Fourth moment Theorem
On finite mixtures of Discretized Beta model for ordered responses
Full text linkThe paper discusses the specification of finite mixture models based on the Discretized Beta distribution for the analysis of ordered discrete responses, as ratings and count data. The ultimate goal of the paper is to parameterize clusters of opposite and intermediate response outcomes. After a thorough discussion on model interpretation, identifiability and estimation, the proposal is illustrated on the wake of a case study on the probability to vote for German Political Parties and with a comparative discussion with the state of the art
Cumulants via diagonal measures
No full textIn the framework of the combinatorial approach to stochastic integration initiated by Rota and Wallstrom, we focus on the representation of cumulants as the expectation of the diagonal measures of the associated product random measure. This setting turns out to be particularly suitable to manage cumulants of the process of variations of a càdlàg Lévy process, as well as to describe k-statistics and polykays for multiplicative random measures
Uncertainty Diagnostics of Binomial Regression Trees for Ordered Rating Data
Full text linkThe paper proposes a method to perform diagnostics of model-based trees for preference and evaluation data on the basis of surrogate residual analysis for ordinal data models. The discussion stems from the introduction of binomial regression trees and discusses how to perform local diagnostics of misspecification against alternative model extensions within the framework of mixture models with uncertainty. Three case studies concerning customer satisfaction and perceived trust for information sources illustrate usefulness and versatile applicative extent of the proposal
A Proposal for a Model-Based Composite Indicator: Experience on Perceived Discrimination in Europe
No full textIn social sciences the need often arises to compare and rank groups of respondents by analyzing huge amounts of data and composite indicators are amongst the most effective tools. The paper aims to design an original procedure suitable for ordinal data and able to synthesize subjective evaluations while accounting for both agreement and heterogeneity in response patterns. A composite indicator for ordinal data based on cub models is introduced: the proposal discloses and preserves the heterogeneity also at an aggregated level. Empirical evidence relies on perceived discrimination analysis stemming from the Special Eurobarometer Survey 2015
Mixture models for analysing ranking data on sport preferences
No full textThe contribution considers a class of mixture models able to interpret empirical evidence about the relationships among motivations, respondents' characteristics and expressed evaluations on the preferred sports. The approach examines and compares the uncertainty of
the answers and the feeling towards the sports by accounting for emph{inflated} categories. Specifically, a new mixture model for dealing with two modal values at the extreme categories is introduced based on a distribution for rank data. After a brief review of the methods, the proposal is discussed on the basis of a survey on sports ranking
The class of CUB models: statistical foundations, inferential issues and empirical evidence
No full textThis paper discusses a general framework for the analysis of rating and preference data that is rooted on a class of mixtures of discrete random variables. These models have been extensively studied and applied in the last 15 years thanks to a flexible and parsimonious parametrization of data generating process and to prompt interpretation of results. The approach considers the final response as the combination of feeling and uncertainty, by allowing for finer model specifications to include refuge options, response styles and possible overdispersion, also in relation to subjects’ and objects’ covariates. The article establishes the state of art of the research inherent to this paradigm, in terms of methodology, inferential procedures and fitting measures, by emphasizing capabilities and limitations yet establishing new findings. In particular, explicative power and predictive performances of cub statistical models for ordinal data are examined and new topics that could boost and support the modelling of uncertainty in this framework are provided. Possible developments are outlined throughout the whole presentation and final comments conclude the paper
Una distribuzione discreta per insegnare inferenza
No full textNei corsi universitari di Statistica, per evitare che la disciplina si esaurisca in un insieme di strumenti esplorativi seguiti da alcuni esercizi di probabilità, è essenziale affrontare lo studio dell’Inferenza e delle sue principali procedure allo scopo di informare gli studenti sulle ragioni per cui questa scienza si trovi oggi in una posizione pervasiva rispetto a tutte le altre discipline. Un momento iniziale è l’introduzione del concetto di campione casuale e la necessità di riassumere le informazioni campionarie ottenute sulle unità statistiche in una quantità singola, definita “statistica” , mediante la quale le procedure di stima, test delle ipotesi e intervalli di confidenza possono essere esemplificate. A questo punto, studenti con un ridotto background matematico trovano un serio ostacolo quando si tratta di applicare le nozioni studiate a distribuzioni statistiche presentate come modelli di problemi reali. Se si esclude il caso della variabile di Bernoulli è difficile ritrovare nei testi usuali esempi di famiglie di distribuzioni che non richiedano calcoli più complessi, nozioni di analisi combinatoria ovvero, nel caso di variabili casuali continue, un’adeguata conoscenza del calcolo integrale. Solo in pochi esempi
si possono sviluppare tutte le tematiche dell’inferenza senza sottoporre gli studenti ad elaborazioni algebriche o analitiche talvolta impegnative. Lo scopo del lavoro è presentare le tematiche essenziali dell’inferenza attraverso una semplice variabile casuale discreta, qui introdotta, e tramite la quale saranno discusse ed esemplificate tutte le procedure inferenziali classiche. In particolare, si mostrerà che
essa è il risultato di un processo generatore dei dati elementare che, a sua volta, può essere generalizzato. Si vedrà, poi, che la distribuzione così definita può essere estesa ad una più ampia famiglia di variabili casuali che possono generare ulteriori esemplificazioni,
alternative rispetto a quella qui analizzata, semplicemente modificando il valore di opportuni parametri. Il lavoro è così organizzato : la Sezione 2 è dedicata ad un’analisi della distribuzione introdotta e finalizzata a determinarne varie proprietà nel suo spazio parametrico ; la Sezione 3 introduce il campionamento casuale ed i principali strumenti necessari per l’inferenza statistica. La Sezione 4 è dedicata ai vari metodi di stima e la Sezione 5 è relativa al test delle ipotesi. Infine, un esempio numerico che ripercorre i contenuti esposti è presentato nella Sezione 6. Alcune considerazioni finali concludono il lavoro
Analysing sport data with clusters of opposite preferences
No full textIn the analysis of questionnaire-based evaluation of sport preferences, measurements of sport participation, opinions on social implications such as resurgence of racism, violence in stadiums and doping, the need arises to establish connections among motivations, subjects’ characteristics and responses. In this setting, the article deals with a selection of statistical models suitable to analyse sport rating data in which clusters of opposite responses are observed. Specifically, a two-component mixture of inverse hypergeometric (MIHG) distributions will be introduced and tested against competing models in order to yield a multifold interpretation of results. The ultimate comparative analysis will consider discrete models with a specific focus on those accounting for both uncertainty and feeling of self-evaluation in presence of inflation at the extreme categories. After a brief review of the methods, the proposal will be discussed both on ranking and rating data on the basis of two surveys on sport preferences and on measurements of sport activity: the identification of clusters of respondents with opposite choices will be investigated also in terms of covariates by comparing fitting performances of the selected models. The conclusions and insights offered by the study can be exploited to design plans of action for some specific policy or marketing strategy
Composite Indicators for Ordinal Data
No full textproposta di costruzione di indicatori compositi in una prospettiva model-base
- …
