191 research outputs found
Noisy Independent Factor Analysis Model for Density Estimation and Classification
No full textWe consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by a number of latent independent components having unknown distributions and are observed in Gaussian noise. We do not assume that either the number of components or the matrix mixing the components are known. We show that the densities of this form can be estimated with a fast rate. Using the mirror averaging aggregation algorithm, we construct a density estimator which achieves a nearly parametric rate (log1/4 n)/√n, independent of the dimensionality of the data, as the sample size n tends to infinity. This estimator is adaptive to the number of components, their distributions and the mixing matrix. We then apply this density estimator to construct nonparametric plug-in classifiers and show that they achieve the best obtainable rate of the excess Bayes risk, to within a logarithmic factor independent of the dimension of the data. Applications of this classifier to simulated data sets and to real data from a remote sensing experiment show promising results.Financial support from the IAP research network of the Belgian government (Belgian Federal Science
Policy) is gratefully acknowledged. Research of A. Samarov was partially supported by NSF grant DMS-
0505561 and by a grant from Singapore-MIT Alliance (CSB). Research of A.B. Tsybakov was partially
supported by the grant ANR-06-BLAN-0194 and by the PASCAL Network of Excellence
Thermodynamic Insights on the structure‐property relationships in substituted benzenes: are the pairwise interactions in tri‐substituted methyl‐nitro‐benzoic acids still valid?
No full textA comprehensive experimental thermochemical study of nine methyl‐substituted nitrobenzoic acids was carried out, leading to the final standard molar enthalpies of formation in the gas phase. The combustion energies were measured using high‐precision combustion calorimetry, and the enthalpies of formation of the crystal phase were derived. The sublimation enthalpies were obtained from the vapor pressure‐temperature dependencies measured using the classic Knudsen effusion mass loss and the transpiration methods. The standard molar enthalpies of vaporisation were derived from the temperature dependence of the mass‐loss rates measured using the non‐isothermal thermogravimetry. The thermal behaviour, including melting temperatures and standard molar enthalpies of fusion, was investigated by DSC. The high‐level quantum chemical G* methods were used for the mutual validation of the experimental and theoretical gas phase enthalpies of formation of methyl‐substituted nitrobenzoic acids. The consistent set of experimental properties at the reference temperature T = 298 K was evaluated and recommended for thermochemical calculations. The pairwise interactions of the substituents on the benzene ring were derived from nitro‐toluenes, methyl‐benzoic acids and nitro‐benzoic acids available in the literature, and the additivity of the contributions when three substituents are placed simultaneously in the benzene ring was discussed
Adaptive Semiparametric Estimation of the Memory Parameter
No full textIn Giraitis, Robinson, and Samarov (1997), we have shown that the optimal rate for memory parameter estimators in semiparametric long memory models with degree of "local smoothness" [beta] is n-r([beta]), r([beta])=[beta]/(2[beta]+1), and that a log-periodogram regression estimator (a modified Geweke and Porter-Hudak (1983) estimator) with maximum frequency m=m([beta])[asymptotically equal to]n2r([beta]) is rate optimal. The question which we address in this paper is what is the best obtainable rate when [beta] is unknown, so that estimators cannot depend on [beta]. We obtain a lower bound for the asymptotic quadratic risk of any such adaptive estimator, which turns out to be larger than the optimal nonadaptive rate n-r([beta]) by a logarithmic factor. We then consider a modified log-periodogram regression estimator based on tapered data and with a data-dependent maximum frequency m=m([beta]), which depends on an adaptively chosen estimator [beta] of [beta], and show, using methods proposed by Lepskii (1990) in another context, that this estimator attains the lower bound up to a logarithmic factor. On one hand, this means that this estimator has nearly optimal rate among all adaptive (free from [beta]) estimators, and, on the other hand, it shows near optimality of our data-dependent choice of the rate of the maximum frequency for the modified log-periodogram regression estimator. The proofs contain results which are also of independent interest: one result shows that data tapering gives a significant improvement in asymptotic properties of covariances of discrete Fourier transforms of long memory time series, while another gives an exponential inequality for the modified log-periodogram regression estimator.long range dependence, semiparametric model, rates of convergence, adaptive bandwidth selection
Noisy independent factor analysis model for density estimation and classification
No full textAbstract: We consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by a number of latent independent components having unknown distributions and are observed in Gaussian noise. We do not assume that either the number of components or the matrix mixing the components are known. We show that the densities of this form can be estimated with a fast rate. Using the mirror averaging aggregation algorithm, we construct a density estimator which achieves a nearly parametric rate (log 1/4 n)/ √ n, independent of the dimensionality of the data, as the sample size n tends to infinity. This estimator is adaptive * Corresponding author. We then apply this density estimator to construct nonparametric plug-in classifiers and show that they achieve the best obtainable rate of the excess Bayes risk, to within a logarithmic factor independent of the dimension of the data. Applications of this classifier to simulated data sets and to real data from a remote sensing experiment show promising results
A single-index quantile regression model and its estimation
No full textModels with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with probability 1. The resulted estimator of the single-index parametric vector is root-n consistent, asymptotically normal, and based on simulation study, is more efficient than the average derivative method in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). The estimator of the link function converges at the usual rate for nonparametric estimation of a univariate function. As an empirical study, we apply the single-index quantile regression model to Boston housing data. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the housing market
Value creation and co-creaiton in the consumer sphere online retail
No full textMini Dissertation (MBA)--University of Pretoria, 2015.Intense business competitiveness, accelerated by web technological advancement of recent
years, poses challenges for online organisations to remain relevant in the market, while
continuing to serve customers needs and wants, as well as acquire new customers in a cost
effective manner. Nowadays, online consumers possess a much greater bargaining power
and are capable of exercising their consumer choice behaviour to a much larger degree than
in the recent past. An increasing number of academic scholars and business practitioners
maintain, that success of the future business will depend on how organisations manage to
revise their existing business practices and bring the customers into the process of value
co-creation.
The research set out to explore opportunities for value creation and co-creation between
online firms and online consumers. In-depth interviews conducted with 22 participants
provided further insights into the notion of value creation and value co-creation in online
retail. Expansive literature review allowed to form solid academic grounds, upon which the
investigation was built and evolved to its conclusion.
Coupled with theoretical premises, key research findings suggested that online firms can
indeed co-create value with existing customers in the closed-to-firms customer sphere,
where only customer-to-customer interactions take place. Enhancement of customers' value
perception plays key role in the process of value co-creation in the customer sphere. As a
result, online firms may reduce cost on acquiring new customers and consequently excel in
revenue growth and business prosperity.sn2016Gordon Institute of Business Science (GIBS)MBAUnrestricte
- …
