The Annals of Statistics

Minimum Hellinger Distance Estimation of Parameter in the Random Censorship Model

Song Yang

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 579-602.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348112

Digital Object Identifier
doi:10.1214/aos/1176348112

Mathematical Reviews number (MathSciNet)
MR1105837

Zentralblatt MATH identifier
0735.62036

JSTOR
links.jstor.org

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems 62P10: Applications to biology and medical sciences

Keywords
Product-limit estimator censored data martingale stochastic integral weak convergence minimum Hellinger distance estimate asymptotically efficient estimate robust statistics minimax robust

Citation

Yang, Song. Minimum Hellinger Distance Estimation of Parameter in the Random Censorship Model. Ann. Statist. 19 (1991), no. 2, 579--602. doi:10.1214/aos/1176348112. https://projecteuclid.org/euclid.aos/1176348112


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