Geodesic
Tuning of a Bayesian estimator under discrete time observations and unknown transition density
Teoriâ slučajnyh processov, Tome 23 (2018) no. 1, pp. 18-52

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the asymptotic behaviour of a Bayesian parameter estimation method on a compact one-dimensional parameter space. The estimation procedure is considered under discrete observations and unknown transition density. Here, we observe the data with constant time steps and the transition density of the data is approximated by using a kernel density estimation method applied to the Monte Carlo simulations of approximations of the theoretical random variables generating the observations. We estimate the error between the theoretical estimator, which assumes the knowledge of the transition density and its approximation which uses the simulation. We prove the strong consistency of the approximated estimator and find the order of the error. Most importantly, we give a parameter tuning result which relates the number of data, the weak error in the approximation process, the number of the Monte-Carlo simulations and the bandwidth size of the kernel density estimation. A guiding example for this situation is the use of Monte Carlo simulations of the Euler scheme for Bayesian estimation in a diffusion setting.
Keywords: Bayesian estimation
Mots-clés : Diffusion process, Monte Carlo simulation. 
@article{THSP_2018_23_1_a2,
     author = {Arturo Kohatsu-Higa and Nicolas Vayatis and Kazuhiro Yasude},
     title = {Tuning of a {Bayesian} estimator under discrete time observations and unknown transition density},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {18--52},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a2/}
}
TY  - JOUR
AU  - Arturo Kohatsu-Higa
AU  - Nicolas Vayatis
AU  - Kazuhiro Yasude
TI  - Tuning of a Bayesian estimator under discrete time observations and unknown transition density
JO  - Teoriâ slučajnyh processov
PY  - 2018
SP  - 18
EP  - 52
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a2/
LA  - en
ID  - THSP_2018_23_1_a2
ER  - 
%0 Journal Article
%A Arturo Kohatsu-Higa
%A Nicolas Vayatis
%A Kazuhiro Yasude
%T Tuning of a Bayesian estimator under discrete time observations and unknown transition density
%J Teoriâ slučajnyh processov
%D 2018
%P 18-52
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a2/
%G en
%F THSP_2018_23_1_a2
Arturo Kohatsu-Higa; Nicolas Vayatis; Kazuhiro Yasude. Tuning of a Bayesian estimator under discrete time observations and unknown transition density. Teoriâ slučajnyh processov, Tome 23 (2018) no. 1, pp. 18-52. http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a2/