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

TL;DR

This paper develops a weighted empirical likelihood approach for two-sample semiparametric models with various censored data types, providing estimators with proven consistency and asymptotic properties, and enabling goodness-of-fit testing.

Contribution

It introduces a unified weighted empirical likelihood framework for diverse censored data in two-sample semiparametric models, including biased sampling and logistic regression.

Findings

Derived consistent semiparametric maximum likelihood estimators.

Established asymptotic normality of the estimators.

Proved the empirical likelihood ratio follows a chi-squared distribution asymptotically.

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 $\theta_0$ and distribution $F_0$ 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.