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Nonparametric Density Estimation in Hidden Markov Models

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Abstract

Let { X n} be a Markov chain that is either f -mixing or satisfies the Poisson equation.In this note we obtain the convergence rate under L 1 -criterion for bounded functions of the X k 's. And in the hidden Markov model setup { (X n ,Y n ) }we study the kernel estimate of the density of the observed variables { Y n }when a 'stable' status is reached.

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Authors and Affiliations

  1. Departamento de matematica, Universidade de Brasilia, 70910-900, Brasilia-DF, Brazil

    C.C.Y. Dorea

  2. University of Science and Technology of China, Hefei, China

    L.C. Zhao

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  1. C.C.Y. Dorea
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  2. L.C. Zhao
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Dorea, C., Zhao, L. Nonparametric Density Estimation in Hidden Markov Models. Statistical Inference for Stochastic Processes 5, 55–64 (2002). https://doi.org/10.1023/A:1013722215208

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