Estimation of the transition density of a Markov chain

Mathieu Sart

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 3, page 1028-1068
  • ISSN: 0246-0203

Abstract

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We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads to a general model selection theorem from which we derive rates of convergence over a very wide range of possibly inhomogeneous and anisotropic Besov spaces. We also investigate the rates that can be achieved under structural assumptions on the transition density.

How to cite

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Sart, Mathieu. "Estimation of the transition density of a Markov chain." Annales de l'I.H.P. Probabilités et statistiques 50.3 (2014): 1028-1068. <http://eudml.org/doc/272004>.

@article{Sart2014,
abstract = {We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads to a general model selection theorem from which we derive rates of convergence over a very wide range of possibly inhomogeneous and anisotropic Besov spaces. We also investigate the rates that can be achieved under structural assumptions on the transition density.},
author = {Sart, Mathieu},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {adaptive estimation; Markov chain; model selection; robust tests; transition density},
language = {eng},
number = {3},
pages = {1028-1068},
publisher = {Gauthier-Villars},
title = {Estimation of the transition density of a Markov chain},
url = {http://eudml.org/doc/272004},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Sart, Mathieu
TI - Estimation of the transition density of a Markov chain
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 3
SP - 1028
EP - 1068
AB - We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads to a general model selection theorem from which we derive rates of convergence over a very wide range of possibly inhomogeneous and anisotropic Besov spaces. We also investigate the rates that can be achieved under structural assumptions on the transition density.
LA - eng
KW - adaptive estimation; Markov chain; model selection; robust tests; transition density
UR - http://eudml.org/doc/272004
ER -

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