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

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

2008-03-12

arxiv.org/abs/0803.1752v1

Annals of Statistics 2008, Vol. 36, No. 1, 147-166

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000695 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000695

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.

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