Asymptotic distribution of the conditional regret risk for selecting good exponential populations

Shanti S. Gupta; Friedrich Liese

Kybernetika (2000)

  • Volume: 36, Issue: 5, page [571]-588
  • ISSN: 0023-5954

Abstract

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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 - λ / 2 ) , 0 < λ ≤ 2 . The aim of this paper is to study the asymptotic behavior of the conditional regret risk ℛ n . It is shown that n ℛ n tends in distribution to a linear combination of independent χ 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 ε > 0 . This probability characterizes the information contained in the historical data.

How to cite

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Gupta, Shanti S., and Liese, Friedrich. "Asymptotic distribution of the conditional regret risk for selecting good exponential populations." Kybernetika 36.5 (2000): [571]-588. <http://eudml.org/doc/33503>.

@article{Gupta2000,
abstract = {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 $\{\mathcal \{R\}\}_\{n\}$. It is shown that $n\{\mathcal \{R\}\}_\{n\}$ 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.},
author = {Gupta, Shanti S., Liese, Friedrich},
journal = {Kybernetika},
keywords = {Bayes method},
language = {eng},
number = {5},
pages = {[571]-588},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Asymptotic distribution of the conditional regret risk for selecting good exponential populations},
url = {http://eudml.org/doc/33503},
volume = {36},
year = {2000},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 5
SP - [571]
EP - 588
AB - 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 ${\mathcal {R}}_{n}$. It is shown that $n{\mathcal {R}}_{n}$ 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.
LA - eng
KW - Bayes method
UR - http://eudml.org/doc/33503
ER -

References

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