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December 2006 Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data
David Donoho, Jiashun Jin
Ann. Statist. 34(6): 2980-3018 (December 2006). DOI: 10.1214/009053606000000920


We apply FDR thresholding to a non-Gaussian vector whose coordinates Xi, i=1, …, n, are independent exponential with individual means μi. The vector μ=(μi) 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 per-coordinate mean-squared error in recovering log(μi), and study minimax estimation over parameter spaces defined by constraints on the per-coordinate p-norm of log(μi), $\frac{1}{n}\sum_{i=1}^{n}\,\log^{p}(\mu_{i})\leq \eta^{p}$.

We show for large n and small η 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.


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David Donoho. Jiashun Jin. "Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data." Ann. Statist. 34 (6) 2980 - 3018, December 2006.


Published: December 2006
First available in Project Euclid: 23 May 2007

zbMATH: 1114.62010
MathSciNet: MR2329475
Digital Object Identifier: 10.1214/009053606000000920

Primary: 62C20 , 62H12
Secondary: 62C10 , 62C12 , 62G20

Keywords: false discovery rate (FDR) , minimax Bayes estimation , minimax decision theory , mixtures of exponential model , Multiple comparisons , Sparsity , threshold rules

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 6 • December 2006
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