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Reconstruction of a low-rank matrix in the presence of Gaussian noise

Shabalin, Andrey A.; Nobel, Andrew B. - In: Journal of Multivariate Analysis 118 (2013) C, pp. 67-76

This paper addresses the problem of reconstructing a low-rank signal matrix observed with additive Gaussian noise. We first establish that, under mild assumptions, one can restrict attention to orthogonally equivariant reconstruction methods, which act only on the singular values of the observed...

Persistent link: https://www.econbiz.de/10010665701

Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA

Jung, Sungkyu; Sen, Arusharka; Marron, J.S. - In: Journal of Multivariate Analysis 109 (2012) C, pp. 190-203

In High Dimension, Low Sample Size (HDLSS) data situations, where the dimension d is much larger than the sample size n … be of the order dα, where α<, =, or >1. Earlier results show the conditions for consistency and strong inconsistency of … PCA in the HDLSS asymptotics. While the results hold under a general situation, the limiting distributions under Gaussian …

Persistent link: https://www.econbiz.de/10011042061

Direct variable selection for discrimination among several groups

Nkiet, Guy Martial - In: Journal of Multivariate Analysis 105 (2012) 1, pp. 151-163

We propose a criterion for variable selection in discriminant analysis. This criterion permits to arrange the variables in decreasing order of adequacy for discrimination, so that the variable selection problem reduces to that of the estimation of suitable permutation and dimensionality. Then,...

Persistent link: https://www.econbiz.de/10010572276

Asymptotic Expansions for Large Deviation Probabilities of Noncentral Generalized Chi-Square Distributions

Richter, W. -D.; Schumacher, J. - In: Journal of Multivariate Analysis 75 (2000) 2, pp. 184-218

Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these...

Persistent link: https://www.econbiz.de/10005006403

PCA consistency for the power spiked model in high-dimensional settings

Yata, Kazuyoshi; Aoshima, Makoto - In: Journal of Multivariate Analysis 122 (2013) C, pp. 334-354

-data-matrix methodology under the power spiked model. We show that the new PCA methods can enjoy consistency properties not only for …

Persistent link: https://www.econbiz.de/10010702809

Correlation tests for high-dimensional data using extended cross-data-matrix methodology

Yata, Kazuyoshi; Aoshima, Makoto - In: Journal of Multivariate Analysis 117 (2013) C, pp. 313-331

In this paper, we consider tests of correlation when the sample size is much lower than the dimension. We propose a new estimation methodology called the extended cross-data-matrix methodology. By applying the method, we give a new test statistic for high-dimensional correlations. We show that...

Persistent link: https://www.econbiz.de/10011042082

Mixtures of common factor analyzers for high-dimensional data with missing information

Wang, Wan-Lun - In: Journal of Multivariate Analysis 117 (2013) C, pp. 120-133

Mixtures of common factor analyzers (MCFA), thought of as a parsimonious extension of mixture factor analyzers (MFA), have recently been developed as a novel approach to analyzing high-dimensional data, where the number of observations n is not very large relative to their dimension p. The key...

Persistent link: https://www.econbiz.de/10010665708

A study of the effect of kurtosis on discriminant analysis under elliptical populations

Arevalillo, Jorge M.; Navarro, Hilario - In: Journal of Multivariate Analysis 107 (2012) C, pp. 53-63

This paper is concerned with the role some parameters indexing four important families within the multivariate elliptically contoured distributions play as indicators of multivariate kurtosis. The problem is addressed for the exponential power family, for a subclass of the Kotz family and for...

Persistent link: https://www.econbiz.de/10010572290

The analysis of distance of grouped data with categorical variables: Categorical canonical variate analysis

Le Roux, Niël J.; Gardner-Lubbe, Sugnet; Gower, John C. - In: Journal of Multivariate Analysis 132 (2014) C, pp. 9-24

We use generalised biplots to develop the important special case of (i) when all variables are categorical and (ii) the samples fall into K recognised groups. We term this Categorical Canonical Variate Analysis (CatCVA), because it has similar characteristics to Rao’s Canonical Variate...

Persistent link: https://www.econbiz.de/10011042056

High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis

He, Xuming; Fung, Wing K. - In: Journal of Multivariate Analysis 72 (2000) 2, pp. 151-162

We consider S-estimators of multivariate location and common dispersion matrix in multiple populations. Instead of averaging the robust estimates of the individual covariance matrices, as used by Todorov, Neykov and Neytchev (1990), the observations are pooled for estimating the common...

Persistent link: https://www.econbiz.de/10005221677