Adaptive estimation of the transition density of a particular hidden Markov chain

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Lacour, Claire

关键词: hidden Markov chain;    transition density;    nonparametric estimation;    deconvolution;    model selection;    rate of convergence;   

DOI  :  10.1016/j.jmva.2007.04.006

来源: Elsevier

【 摘 要 】

We study the following model of hidden Markov chain: Y-i = X-i + epsilon(i), i = 1,...,n + 1 with (X-i) a real-valued positive recurrent and stationary Markov chain, and (epsilon(i)) l <= i <= n+1 (X-i) having a known distribution. We present an adaptive estimator of the transition density based on the quotient of a deconvolution estimator of the density of X-i and an estimator of the density of (X-i, Xi+1). These estimators are obtained by contrast minimization and model selection. We evaluate the L-2 risk and its rate of convergence for ordinary smooth and supersmooth noise with regard to ordinary smooth and supersmooth chains. Some examples are also detailed. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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