Admissible predictive density estimation

Brown, Lawrence D.; George, Edward I.; Xu, Xinyi

Brown, Lawrence D. ; George, Edward I. ; Xu, Xinyi

Ann. Statist., Tome 36 (2008) no. 1, p. 1156-1170 / Harvested from Project Euclid

Résumé

Let X|μ∼N_p(μ, v_xI) and Y|μ∼N_p(μ, v_yI) be independent p-dimensional multivariate normal vectors with common unknown mean μ. Based on observing X=x, we consider the problem of estimating the true predictive density p(y|μ) of Y under expected Kullback–Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205–230] are sufficient for a formal Bayes rule to be admissible.

Publié le : 2008-06-15
Classification: Admissibility, Bayesian predictive distribution, complete class, prior distributions, 62C15, 62C07, 62C10, 62C20

@article{1211819560,
     author = {Brown, Lawrence D. and George, Edward I. and Xu, Xinyi},
     title = {Admissible predictive density estimation},
     journal = {Ann. Statist.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 1156-1170},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1211819560}
}

Brown, Lawrence D.; George, Edward I.; Xu, Xinyi. Admissible predictive density estimation. Ann. Statist., Tome 36 (2008) no. 1, pp.  1156-1170. http://gdmltest.u-ga.fr/item/1211819560/