Multiple Testing in Nonparametric Hidden Markov Models: An Empirical Bayes Approach
Multiple Testing in Nonparametric Hidden Markov Models: An Empirical Bayes Approach
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发表时间：
2021-01
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通讯作者：
Kweku Abraham;I. Castillo;E. Gassiat
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作者：
Kweku Abraham;I. Castillo;E. Gassiat
给出了一个具有两个状态的非参数隐马尔可夫模型（HMM），考虑了构造有效的多重检验程序的问题，将其中一个状态视为未知的零假设。介绍了一个程序，基于非参数经验贝叶斯的想法，控制在用户指定的水平的错误发现率（FDR）。还以控制真阳性率的形式提供功率保证。在建设中的关键步骤之一，要求上确界-范数收敛的HMM的发射密度的初步估计。我们提供了这样的估计的存在性，收敛在最佳的极小极大率，对于一个HMM的情况下，与$J\ge 2$状态，这是独立的兴趣。
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.