Effects of statistical dependence on multiple testing under a hidden Markov model

Details Effects of statistical dependence on multiple testing under a hidden Markov model Effects of statistical dependence on multiple testing under a hidden Markov model

2009-04-09

arxiv.org/abs/0904.1551v3

Annals of Statistics 2011, Vol. 39, No. 1, 439-473

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS822 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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