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arXiv · 2101.03838

Multiple Testing in Nonparametric Hidden Markov Models: An Empirical Bayes Approach

Kweku Abraham·Ismael Castillo·Elisabeth Gassiat
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Abstract

Given a nonparametric Hidden Markov Model (HMM) with two states, the question of constructing efficient multiple testing procedures is considered, treating one of the states as an unknown null hypothesis. A procedure is introduced, based on nonparametric empirical Bayes ideas, that controls the False Discovery Rate (FDR) at a user--specified level. Guarantees on power are also provided, in the form of a control of the true positive rate. One of the key steps in the construction requires supremum--norm convergence of preliminary estimators of the emission densities of the HMM. We provide the existence of such estimators, with convergence at the optimal minimax rate, for the case of a HMM with $J\ge 2$ states, which is of independent interest.

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Kweku Abraham, Ismael Castillo, Elisabeth Gassiat. 2021-01-11. Multiple Testing in Nonparametric Hidden Markov Models: An Empirical Bayes Approach. https://arxiv.org/abs/2101.03838

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