Estimating the Proportion of Nonzero Normal Means under Certain Strong Covariance Dependence
Year: 2012
Type: preprint
Abstract: The proportion of true null (or false null) hypotheses is a critical ingredient of an adaptive multiple testing procedure since it directly influences the false discovery rate of the procedure and a tighter estimator of this quantity usually increases the power of the procedure. However, in general it is very hard to well estimate this proportion under strong dependence. For the multiple testing scenario where the test statistics are jointly normally distributed and we are interested in assessing which of them have zero means, we construct a consistent estimator of the proportion of test statistics that have nonzero means (i.e., the proportion of nonzero normal means) when the correlation matrix of these statistics is known but the dependence among them can be fairly strong. Our estimator is perhaps the first among estimators of this proportion that has theoretically ensured consistency under strong dependence, and it provides a partial, positive answer to the question raised by Jianqing Fan and his colleagues on if it is possible to estimate the proportion of nonzero normal means under arbitrary covariance dependence. We demonstrate via numerical studies that the new estimator is very competitive to existing estimators of this proportion but performs much better in terms of precision and stability when the nonzero normal means are large, or rare and small.
Source: arXiv (Cornell University)
Author: Xiongzhi Chen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2129162023