Estimating the Proportion of True Null Hypotheses, . . .

Estimating the Proportion of True Null Hypotheses, . . . (2003)

by Egil Ferkingstad , Mette Langaas , Bo Lindqvist

Datum	Value	Source
TITLE	Summary	SVM HeaderParse 0.1
AUTHOR NAME	Egil Ferkingstad	SVM HeaderParse 0.1
AUTHOR NAME	Mette Langaas	SVM HeaderParse 0.1
AUTHOR NAME	Bo Lindqvist	SVM HeaderParse 0.1
ABSTRACT	The problem of estimating the proportion, ¢ ¡ , of true null hypotheses is important in cases where a large number of hypothesis tests are performed. In addition to being an interesting quantity in itself, the estimate of ¡ can be used as an input to methods for assessing or controlling error rates such as the family wise error rate and the false discovery rate (Benjamini and Hochberg 1995). On the basis of the observed p-values corresponding to the hypothesis tests, several estimators of ¡ are described. Schweder and Spjøtvoll’s (1982) nonparametric estimator of is studied, and different estimators based on estimating the p-value density are developed. Original contributions in this work include a new estimator of ¡ based on Grenander’s (1956) nonparametric maximum likelihood density estimator, a novel application of convex decreasing density estimation to the problem of estimating ¢ ¡ , and the use of kernel density estimation with a choice of smoothing parameter especially tailored to estimate £ ¡. The estimators are derived under the assumption of independent p-values, and evaluated on simulated data with different degree	SVM HeaderParse 0.1
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