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2008 Least squares type estimation of the transition density of a particular hidden Markov chain
Claire Lacour
Electron. J. Statist. 2: 1-39 (2008). DOI: 10.1214/07-EJS111


In this paper, we study the following model of hidden Markov chain: Yi=Xi+ɛi, i=1,,n+1 with (Xi) a real-valued stationary Markov chain and (ɛi)1in+1 a noise having a known distribution and independent of the sequence (Xi). We present an estimator of the transition density obtained by minimization of an original contrast that takes advantage of the regressive aspect of the problem. It is selected among a collection of projection estimators with a model selection method. The L2-risk and its rate of convergence are evaluated for ordinary smooth noise and some simulations illustrate the method. We obtain uniform risk bounds over classes of Besov balls. In addition our estimation procedure requires no prior knowledge of the regularity of the true transition. Finally, our estimator permits to avoid the drawbacks of quotient estimators.


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Claire Lacour. "Least squares type estimation of the transition density of a particular hidden Markov chain." Electron. J. Statist. 2 1 - 39, 2008.


Published: 2008
First available in Project Euclid: 16 January 2008

zbMATH: 1135.62064
MathSciNet: MR2369084
Digital Object Identifier: 10.1214/07-EJS111

Primary: 62G05
Secondary: 62H12 , 62M05

Keywords: Hidden Markov chain , Model selection , nonparametric estimation , rate of convergence , Transition density

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society


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