Nous étudions les propriétés asymptotiques des lois a posteriori lorsque la distribution des observations est mal spécifiée, c'est-à-dire lorsque la loi a posteriori est construite à partir d'une famille de densités où , alors que la vraie loi des observations peut ne correspondre à aucune densité hσ. Nous obtenons des propriétés de concentration de la loi a posteriori autour d'une valeur fixe du paramètre ainsi que des propriétés de concentration autour de l'estimateur du maximum de vraisemblance.
We investigate the asymptotic properties of posterior distributions when the model is misspecified, i.e. it is contemplated that the observations x1,…,xn might be drawn from a density in a family where , while the actual distribution of the observations may not correspond to any of the densities hσ. A concentration property around a fixed value of the parameter is obtained as well as concentration properties around the maximum likelihood estimate.
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@article{CRMATH_2002__335_5_495_0, author = {Abraham, Christophe and Cadre, Beno{\i}̂t}, title = {Asymptotic properties of posterior distributions derived from misspecified models}, journal = {Comptes Rendus. Math\'ematique}, pages = {495--498}, publisher = {Elsevier}, volume = {335}, number = {5}, year = {2002}, doi = {10.1016/S1631-073X(02)02520-7}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02520-7/} }
TY - JOUR AU - Abraham, Christophe AU - Cadre, Benoı̂t TI - Asymptotic properties of posterior distributions derived from misspecified models JO - Comptes Rendus. Mathématique PY - 2002 SP - 495 EP - 498 VL - 335 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02520-7/ DO - 10.1016/S1631-073X(02)02520-7 LA - en ID - CRMATH_2002__335_5_495_0 ER -
%0 Journal Article %A Abraham, Christophe %A Cadre, Benoı̂t %T Asymptotic properties of posterior distributions derived from misspecified models %J Comptes Rendus. Mathématique %D 2002 %P 495-498 %V 335 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02520-7/ %R 10.1016/S1631-073X(02)02520-7 %G en %F CRMATH_2002__335_5_495_0
Abraham, Christophe; Cadre, Benoı̂t. Asymptotic properties of posterior distributions derived from misspecified models. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 495-498. doi : 10.1016/S1631-073X(02)02520-7. http://www.numdam.org/articles/10.1016/S1631-073X(02)02520-7/
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