Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data
成果类型：
Article
署名作者：
Donoho, David; Jin, Jiashun
署名单位：
Stanford University; Purdue University System; Purdue University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053606000000920
发表日期：
2006
页码：
2980-3018
关键词：
摘要：
We apply FDR thresholding to a non-Gaussian vector whose coordinates X-i, i = 1,..., n, are independent exponential with individual means mu(i). The vector mu = (mu(i)) is thought to be sparse, with most coordinates 1 but a small fraction significantly larger than 1; roughly, most coordinates are simply 'noise,' but a small fraction contain 'signal.' We measure risk by percoordinate mean-squared error in recovering log(mu(i)), and study minimax estimation over parameter spaces defined by constraints on the per-coordinate p-norm of log(mu(i)), 1/n Sigma(n)(i=1) log(p) (mu(i)) <= eta(p) . We show for large n and small q that FDR thresholding can be nearly minimax. The FDR control parameter 0 < q < 1 plays an important role: when q <= 1/2, the FDR estimator is nearly minimax, while choosing a fixed q > 1/2 prevents near minimaxity. These conclusions mirror those found in the Gaussian case in Abramovich et al. [Ann. Statist. 34 (2006) 584-653]. The techniques developed here seem applicable to a wide range of other distributional assumptions, other loss measures and non-i.i.d. dependency structures.