Mathematics – Statistics Theory
Scientific paper
2010-01-11
Annals of Statistics 2010, Vol. 38, No. 1, 100-145
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS696 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS696
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several important problems, including the evaluation of the minimax rate of convergence and the construction of rate-optimal estimators, remain open. In this paper, we consider optimal estimation of the null density and the proportion of nonnull effects. Both minimax lower and upper bounds are derived. The lower bound is established by a two-point testing argument, where at the core is the novel construction of two least favorable marginal densities $f_1$ and $f_2$. The density $f_1$ is heavy tailed both in the spatial and frequency domains and $f_2$ is a perturbation of $f_1$ such that the characteristic functions associated with $f_1$ and $f_2$ match each other in low frequencies. The minimax upper bound is obtained by constructing estimators which rely on the empirical characteristic function and Fourier analysis. The estimator is shown to be minimax rate optimal. Compared to existing methods in the literature, the proposed procedure not only provides more precise estimates of the null density and the proportion of the nonnull effects, but also yields more accurate results when used inside some multiple testing procedures which aim at controlling the False Discovery Rate (FDR). The procedure is easy to implement and numerical results are given.
Cai Tony T.
Jin Jiashun
No associations
LandOfFree
Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-719042