The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain's current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent nonparametric estimate of the entropy for these iterative densities. This theoretical study can be viewed as a building block for a more general MCMC evaluation tool grounded on such estimates.
Mots-clés : entropy, Kullback divergence, Metropolis-Hastings algorithm, nonparametric statistic
@article{PS_2013__17__419_0,
author = {Chauveau, Didier and Vandekerkhove, Pierre},
title = {Smoothness of {Metropolis-Hastings} algorithm and application to entropy estimation},
journal = {ESAIM: Probability and Statistics},
pages = {419--431},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2012004},
mrnumber = {3066386},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2012004/}
}
TY - JOUR AU - Chauveau, Didier AU - Vandekerkhove, Pierre TI - Smoothness of Metropolis-Hastings algorithm and application to entropy estimation JO - ESAIM: Probability and Statistics PY - 2013 SP - 419 EP - 431 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2012004/ DO - 10.1051/ps/2012004 LA - en ID - PS_2013__17__419_0 ER -
%0 Journal Article %A Chauveau, Didier %A Vandekerkhove, Pierre %T Smoothness of Metropolis-Hastings algorithm and application to entropy estimation %J ESAIM: Probability and Statistics %D 2013 %P 419-431 %V 17 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2012004/ %R 10.1051/ps/2012004 %G en %F PS_2013__17__419_0
Chauveau, Didier; Vandekerkhove, Pierre. Smoothness of Metropolis-Hastings algorithm and application to entropy estimation. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 419-431. doi : 10.1051/ps/2012004. http://www.numdam.org/articles/10.1051/ps/2012004/
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