Title

Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

Authors

Authors

J. J. Ren

Comments

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Abbreviated Journal Title

Bernoulli

Keywords

bootstrap; doubly censored data; empirical likelihood; interval censored; data; partly interval censored data; right censored data; DOUBLY CENSORED-DATA; SELF-CONSISTENT ESTIMATORS; FAILURE TIME MODEL; GOODNESS-OF-FIT; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC PROPERTIES; BOOTSTRAP; TESTS; CHOICE; Statistics & Probability

Abstract

Thus far, likelihood-based interval estimates for quantiles have not been studied in the literature on interval censored case 2 data and partly interval censored data, and, in this context, the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval censored data. The fourth order expansion of the weighted empirical log-likelihood ratio is derived and the theoretical coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least 'first order' accuracy. In particular, for right censored data, we show that the coverage accuracy is at least O(n(-1/2)) and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally provides a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate n(-1/3), the weighted empirical log-likelillood ratio has an asymptotic distribution completely different from that obtained by the empirical likelihood approach and the resulting WELRCI perform favorably in the available comparison simulation studies.

Journal Title

Bernoulli

Volume

14

Issue/Number

3

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

725

Last Page

748

WOS Identifier

WOS:000264166300007

ISSN

1350-7265

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