Joint adaptive mean-variance regularization and variance stabilization of high dimensional data

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• 作者：Jean-Eudes Dazard^a ; ^{jxd101@case.edu} ; J. Sunil Rao^b ; ^{JRao@med.miami.edu}
• 关键词：Bioinformatics ; Inadmissibility ; Regularization ; Shrinkage estimators ; Normalization ; Variance stabilization
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：July, 2012
• 卷：56
• 期：7
• 页码：2317-2333
• 文件大小：1248 K

摘要

The paper addresses a common problem in the analysis of high-dimensional high-throughput 鈥渙mics鈥?data, which is parameter estimation across multiple variables in a set of data where the number of variables is much larger than the sample size. Among the problems posed by this type of data are that variable-specific estimators of variances are not reliable and variable-wise tests statistics have low power, both due to a lack of degrees of freedom. In addition, it has been observed in this type of data that the variance increases as a function of the mean. We introduce a non-parametric adaptive regularization procedure that is innovative in that (i) it employs a novel 鈥渟imilarity statistic鈥?based clustering technique to generate local-pooled or regularized shrinkage estimators of population parameters, (ii) the regularization is done jointly on population moments, benefiting from C. Stein鈥檚 result on inadmissibility, which implies that usual sample variance estimator is improved by a shrinkage estimator using information contained in the sample mean. From these joint regularized shrinkage estimators, we derived regularized t-like statistics and show in simulation studies that they offer more statistical power in hypothesis testing than their standard sample counterparts, or regular common value-shrinkage estimators, or when the information contained in the sample mean is simply ignored. Finally, we show that these estimators feature interesting properties of variance stabilization and normalization that can be used for preprocessing high-dimensional multivariate data. The method is available as an R package, called 鈥楳VR鈥?(鈥楳ean-Variance Regularization鈥?, downloadable from the CRAN website.