## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Weighted Empirical Likelihood in Some Two-Sample Semiparametric Models with Various Types of Censored Data

Jian-Jian Ren
The Annals of Statistics
Vol. 36, No. 1 (Feb., 2008), pp. 147-166
Stable URL: http://www.jstor.org/stable/25464619
Page Count: 20
Preview not available

## 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 $(\tilde{\theta}_{n},\tilde{F}_{n})$ for the underlying parameter θ₀ and distribution F₀ is derived, and the strong consistency of $(\tilde{\theta}_{n},\tilde{F}_{n})$ and the asymptotic normality of $\tilde{\theta}_{n}$ 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 $\sqrt{n}(\tilde{F}_{n}-F_{0})$ weakly converges to a centered Gaussian process, which leads to a consistent goodness-of-fit test for the case-control logistic regression models.

• 147
• 148
• 149
• 150
• 151
• 152
• 153
• 154
• 155
• 156
• 157
• 158
• 159
• 160
• 161
• 162
• 163
• 164
• 165
• 166