Article (Scientific journals)
ROBUST BAYES-LIKE ESTIMATION: RHO-BAYES ESTIMATION
Baraud, Yannick; Birgé, Lucien
2020In Annals of Statistics
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Keywords :
Bayesian estimation; Robust Estimation; Density Estimation
Abstract :
[en] We observe n independent random variables with joint distribution P and pretend that they are i.i.d. with some common density s (with respect to a known measure μ) that we wish to estimate. We consider a density model S for s that we endow with a prior distribution π (with support in S) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around s whenever the data are truly i.i.d. and their density s belongs to the model S. Furthermore, in this case, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved when the model is misspecified or when the data are not i.i.d. but the marginal densities of their joint distribution are close enough in Hellinger distance to the model S.
Disciplines :
Mathematics
Author, co-author :
Baraud, Yannick ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Birgé, Lucien;  Université Paris-Sorbonne (Paris IV) > Laboratoire de Probabilités, Statistique et Modélisation (LPSM)
External co-authors :
yes
Language :
English
Title :
ROBUST BAYES-LIKE ESTIMATION: RHO-BAYES ESTIMATION
Publication date :
2020
Journal title :
Annals of Statistics
ISSN :
2168-8966
Publisher :
Institute of Mathematical Statistics, Cleveland, United States - Ohio
Peer reviewed :
Peer Reviewed verified by ORBi
European Projects :
H2020 - 811017 - SanDAL - ERA Chair in Mathematical Statistics and Data Science for the University of Luxembourg
Name of the research project :
SanDAL
Funders :
CE - Commission Européenne [BE]
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