Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends on the set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations.

Keywords: hidden Markov model, particle filter, central limit theorem, asymptotic variance, tightness, sequential Monte-Carlo

@article{PS_2012__16__151_0, author = {Favetto, Benjamin}, title = {On the asymptotic variance in the central limit theorem for particle filters}, journal = {ESAIM: Probability and Statistics}, pages = {151--164}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2010019}, mrnumber = {2946125}, zbl = {1273.60046}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2010019/} }

TY - JOUR AU - Favetto, Benjamin TI - On the asymptotic variance in the central limit theorem for particle filters JO - ESAIM: Probability and Statistics PY - 2012 SP - 151 EP - 164 VL - 16 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2010019/ DO - 10.1051/ps/2010019 LA - en ID - PS_2012__16__151_0 ER -

%0 Journal Article %A Favetto, Benjamin %T On the asymptotic variance in the central limit theorem for particle filters %J ESAIM: Probability and Statistics %D 2012 %P 151-164 %V 16 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2010019/ %R 10.1051/ps/2010019 %G en %F PS_2012__16__151_0

Favetto, Benjamin. On the asymptotic variance in the central limit theorem for particle filters. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 151-164. doi : 10.1051/ps/2010019. http://archive.numdam.org/articles/10.1051/ps/2010019/

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