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February 2000 On the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint
Miguel A. Arcones, Francisco J. Samaniego
Ann. Statist. 28(1): 116-150 (February 2000). DOI: 10.1214/aos/1016120367

Abstract

We identify the asymptotic behavior of the estimators proposed by Rojo and Samaniego and Mukerjee of a distribution $F$ assumed to be uniformly stochastically smaller than a known baseline distribution $G$.We show that these estimators are $\sqrt{n}$-convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function. By examining the mean squared error of the limit distribution, we are able to identify the optimal estimator within Mukerjee’s class under a variety of different assumptions on $F$ and $G$. Similar theoretical results are developed for the two-sample problem where$F$ and $G$ are both unknown. The asymptotic distribution theory is applied to obtain confidence bands for the survival function $\bar{F}$ based on published data from an accelerated life testing experiment.

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Miguel A. Arcones. Francisco J. Samaniego. "On the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint." Ann. Statist. 28 (1) 116 - 150, February 2000. https://doi.org/10.1214/aos/1016120367

Information

Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62332
MathSciNet: MR1762906
Digital Object Identifier: 10.1214/aos/1016120367

Subjects:
Primary: 62G05
Secondary: 62E20 , 62G10

Keywords: Brownian motion , Empirical processes , hazard rate ordering , uniform stochastic ordering

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2000
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