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Persistence of plug-in rule in classification of high dimensional multivariate binary data

JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2007年第11期137卷 3687-3705页

作者： Park, Junyong Ghosh, Jayanta K. Univ Maryland Dept Math & Stat Baltimore Country MD 21250 USA Indian Stat Inst Div Theoret Stat & Math Bangalore Karnataka India

In this paper. we consider the classification problem when the predictors are multivariate binary random variables. Variables are modeled as independent. but not necessarily identical, Bernoulli. A triangular array for parameters. (p(11)((n)) ..., p(1d)((n)), p(21)((n)) ..., p(2d)((n))), is assumed to allow parameters to change and the number of the variables, d, to increase for adopting more flexible models as the sample size. it. increases. Our results are obtained under moderate assumptions on the triangular array of the probability vectors. We use maximum likelihood estimators for the parameters and plug them into the Bayes classifier. This is a plug-in classifier, a sort of objective Bayes rule. It is shown in Wilbur et a]. [2002. Variable selection in high-dimensional multivariate binary data with application to the analysis of microbial DNA fingerprints. Biometrics 58, 378-386] via simulations that the plug-in rule classifies quite well even when the assumption of independence is violated. The main interest in this paper is in the complex case of d/n(v) -> c for some v > 0 and c > 0 tor which very little is known. Using linearity of the plug-in rule, we show its persistence, a generalization of the notion of consistency, when the variance of the plug-in rule or a quantity measuring signal to noise ratio is divergent otherwise we show there exists an in example of non-persistence of the plug-in rule. In case of non-persistence, we introduce the notion of sparsity and overcome non-persistence by selecting a subset of the variables. This shows why a variable selection procedure may he effective especially for contemporary practical problems with high dimensional data [Wilbur et al, 2002. Variable selection in high-dimensional multivariate binary data with application to the analysis of microbial DNA *** 58, 378-386]. (C) 2007 Elsevier B.V. All rights reserved.

关键词： persistence triangular arrays high dimensional multivariate binary data plug-in ruled sparsity

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Estimating and testing conditional sums of means in high dimensional multivariate binary data

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2011年第2期141卷 1021-1030页

作者： Park, Junyong Davis, J. Wade Univ Missouri Dept Stat Dept Hlth Management & Informat Columbia MO 65211 USA Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA

We study the estimation of the strength of signals corresponding to the high valued observations in multivariate binary data. These problems can arise in a variety of areas, such as mass spectrometry or function magnetic resonance imaging (fMRI), where the underlying signals could be interpreted as a proxy for biochemical or physiological response to a condition or treatment. More specifically, the problem we consider involves estimating the sum of a collection of binomial probabilities corresponding to large values of the associated binomial random variables. We emphasize the case where the dimension is much greater than the sample size, and most of the probabilities of the events of interest are close to zero. Two estimation approaches are proposed: conditional maximum likelihood and nonparametric empirical Bayes. We use these estimators to construct a test of homogeneity for two groups of high dimensional multivariate binary data. Simulation studies on the size and power of the proposed tests are given, and the tests are demonstrated using mass spectrometry data from a breast cancer study. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Conditional MLE Empirical Bayes high dimensional multivariate binary data Sparsity Mass spectrometry

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Independent rule in classification of multivariate binary data

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JOURNAL OF multivariate ANALYSIS 2009年第10期100卷 2270-2286页

作者： Park, Junyong Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA

We consider the performance of the independent rule in classification of multivariate binary data. In this article, broad studies are presented including the performance of the independent rule when the number of variables, d, is fixed or increased with the sample size, n. The latter situation includes the case of d = O(n(tau)) for tau > 0 which cover "the small sample and the large dimension", namely d >> n when tau > 1. Park and Ghosh [J. Park, J.K. Ghosh, Persistence of plug-in rule in classification of high dimensional binary data, journal of Statistical Planning and Inference 137 (2007) 3687-3707] studied the independent rule in terms of the consistency of misclassification error rate which is called persistence under growing numbers of dimensions, but they did not investigate the convergence rate. We present asymptotic results in view of the convergence rate under some structured parameter space and highlight that variable selection is necessary to improve the performance of the independent rule. We also extend the applications of the independent rule to the case of correlated binary data such as the Bahadur representation and the logit model. It is emphasized that variable selection is also needed in correlated binary data for the improvement of the performance of the independent rule. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Classification Independent rule Sparsity high dimensional multivariate binary data MLE Convergence rate

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