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State-by-state Minimax Adaptive Estimation for Nonparametric Hidden Markov Models. (arXiv:1706.08277v1 [math.ST])
来源于:arXiv
This paper considers the problem of estimating the emission densities of a
nonparametric finite state space hidden Markov model in a way that is
state-by-state adaptive and leads to minimax rates for each emission
density--as opposed to globally minimax estimators, which adapt to the worst
regularity among the emission densities. We propose a model selection procedure
based on the Goldenschluger-Lepski method. Our method is computationally
efficient and only requires a family of preliminary estimators, without any
restriction on the type of estimators considered. We present two such
estimators that allow to reach minimax rates up to a logarithmic term: a
spectral estimator and a least squares estimator. Finally, numerical
experiments assess the performance of the method and illustrate how to
calibrate it in practice. Our method is not specific to hidden Markov models
and can be applied to nonparametric multiview mixture models. 查看全文>>