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Effects of statistical dependence on multiple testing under a hidden Markov model. (English) Zbl 1209.62192
Summary: 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.

MSC:
62M02 Markov processes: hypothesis testing
62H15 Hypothesis testing in multivariate analysis
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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