Title

Weighted empirical likelihood in some two-sample semiparametric models with various types of censored data

Authors

Authors

J. J. Ren

Comments

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Abbreviated Journal Title

Ann. Stat.

Keywords

biased sampling; bootstrap; case-control data; doubly censored data; empirical likelihood; Kolmogorov-Smirnov statistic; interval censored; data; likelihood ratio; logistic regression; maximum likelihood; estimator; partly interval-censored data; right censored data; RATIO CONFIDENCE-INTERVALS; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC; PROPERTIES; SELF-CONSISTENT; ESTIMATORS; DISTRIBUTIONS; BIAS; Statistics & Probability

Abstract

In this article, the weighted empirical likelihood is applied to a general setting of two-sample semiparametric models, which includes biased sampling models and case-control logistic regression models as special cases. For various types of censored data, such as right censored data, doubly censored data, interval censored data and partly interval-censored data, the weighted empirical likelihood-based semiparametric maximum likelihood estimator ((theta) over tilde (n), (F) over tilde (n)) for the underlying parameter theta(0) and distribution F(0) is derived, and the strong consistency of ((theta) over tilde (n), (F) over tilde (n)) and the asymptotic normality of (theta) over tilde (n) are established. Under biased sampling models, the weighted empirical log-likelihood ratio is shown to have an asymptotic scaled chi-squared distribution for censored data aforementioned. For right censored data, doubly censored data and partly interval-censored data, it is shown that root n((F) over tilde (n) - F(0)) weakly converges to a centered Gaussian process, which leads to a consistent goodness-of-fit test for the case-control logistic regression models.

Journal Title

Annals of Statistics

Volume

36

Issue/Number

1

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

147

Last Page

166

WOS Identifier

WOS:000253390000006

ISSN

0090-5364

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