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June, 1991 Minimum Hellinger Distance Estimation of Parameter in the Random Censorship Model
Song Yang
Ann. Statist. 19(2): 579-602 (June, 1991). DOI: 10.1214/aos/1176348112


This paper discusses the minimum Hellinger distance estimation (MHDE) of the parameter that gives the "best fit" of a parametric family to a density when the data are randomly censored. In studying the MHDE, the tail behavior of the product-limit (P-L) process is investigated, and the weak convergence of the process on the real line is established. An upper bound on the mean square increment of the normalized P-L process is also obtained. With these results, the asymptotic behavior of the MHDE is established and it is shown that, when the parametric model is correct, the MHD estimators are asymptotically efficient among the class of regular estimators. This estimation procedure is also minimax robust in small Hellinger neighborhoods of the given parametric family. The work extends the results of Beran for the complete i.i.d. data case to the censored data case. Some of the proofs employ the martingale techniques by Gill.


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Song Yang. "Minimum Hellinger Distance Estimation of Parameter in the Random Censorship Model." Ann. Statist. 19 (2) 579 - 602, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0735.62036
MathSciNet: MR1105837
Digital Object Identifier: 10.1214/aos/1176348112

Primary: 62F35
Secondary: 60F05 , 62E20 , 62P10

Keywords: asymptotically efficient estimate , Censored data , martingale , minimax robust , minimum Hellinger distance estimate , product-limit estimator , robust statistics , stochastic integral , weak convergence

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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