Asymptotic distribution of the conditional regret risk for selecting good exponential populations
Kybernetika, Tome 36 (2000) no. 5, p. [571]
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In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang [10] who proved that the regret risk converges to zero with rate $O(n^{-\lambda /2}),0\lambda \le 2$. The aim of this paper is to study the asymptotic behavior of the conditional regret risk ${\cal R}_{n}$. It is shown that $n{\cal R}_{n}$ tends in distribution to a linear combination of independent $\chi ^{2}$-distributed random variables. As an application we give a large sample approximation for the probability that the conditional regret risk exceeds the Bayes risk by a given $\varepsilon >0.$ This probability characterizes the information contained in the historical data.
@article{KYB_2000__36_5_a4,
author = {Gupta, Shanti S. and Liese, Friedrich},
title = {Asymptotic distribution of the conditional regret risk for selecting good exponential populations},
journal = {Kybernetika},
pages = {[571]},
publisher = {mathdoc},
volume = {36},
number = {5},
year = {2000},
mrnumber = {1882795},
zbl = {1243.62006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_2000__36_5_a4/}
}
TY - JOUR AU - Gupta, Shanti S. AU - Liese, Friedrich TI - Asymptotic distribution of the conditional regret risk for selecting good exponential populations JO - Kybernetika PY - 2000 SP - [571] VL - 36 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/KYB_2000__36_5_a4/ LA - en ID - KYB_2000__36_5_a4 ER -
Gupta, Shanti S.; Liese, Friedrich. Asymptotic distribution of the conditional regret risk for selecting good exponential populations. Kybernetika, Tome 36 (2000) no. 5, p. [571]. http://geodesic.mathdoc.fr/item/KYB_2000__36_5_a4/