Statistics Papers

Document Type

Journal Article

Date of this Version

2007

Publication Source

Journal of the American Statistical Association

Volume

102

Issue

478

Start Page

495

Last Page

506

DOI

10.1198/016214507000000167

Abstract

An important issue raised by Efron in the context of large-scale multiple comparisons is that in many applications, the usual assumption that the null distribution is known is incorrect, and seemingly negligible differences in the null may result in large differences in subsequent studies. This suggests that a careful study of estimation of the null is indispensable. In this article we consider the problem of estimating a null normal distribution, and a closely related problem, estimation of the proportion of nonnull effects. We develop an approach based on the empirical characteristic function and Fourier analysis. The estimators are shown to be uniformly consistent over a wide class of parameters. We investigate the numerical performance of the estimators using both simulated and real data. In particular, we apply our procedure to the analysis of breast cancer and human immunodeficiency virus microarray datasets. The estimators perform favorably compared with existing methods.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 01 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/016214507000000167.

Keywords

characteristic functions, empirical characteristic function, Fourier coefficients, multiple testing, null distribution, proportion of nonnull effects

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Date Posted: 27 November 2017