Open Access
February 2011 Effects of statistical dependence on multiple testing under a hidden Markov model
Zhiyi Chi
Ann. Statist. 39(1): 439-473 (February 2011). DOI: 10.1214/10-AOS822


The performance of multiple hypothesis testing is known to be affected by the statistical dependence among random variables involved. The mechanisms responsible for this, however, are not well understood. We study the effects of the dependence structure of a finite state hidden Markov model (HMM) on the likelihood ratios critical for optimal multiple testing on the hidden states. Various convergence results are obtained for the likelihood ratios as the observations of the HMM form an increasing long chain. Analytic expansions of the first and second order derivatives are obtained for the case of binary states, explicitly showing the effects of the parameters of the HMM on the likelihood ratios.


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Zhiyi Chi. "Effects of statistical dependence on multiple testing under a hidden Markov model." Ann. Statist. 39 (1) 439 - 473, February 2011.


Published: February 2011
First available in Project Euclid: 15 February 2011

zbMATH: 1209.62192
MathSciNet: MR2797853
Digital Object Identifier: 10.1214/10-AOS822

Primary: 62H15 , 62M02

Keywords: contraction , FDR , HMM , multiple hypothesis testing , Nonlinear filtering

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 1 • February 2011
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