Jian-Jian Ren
Department of Mathematics
University of Central Florida
Weighted Empirical Likelihood in Some Two-Sample Semiparametric Models
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 estimators (MLE) qn
and Fn for the underlying parameter q0
and F0 are derived, and their strong consistency
and the asymptotic normality of qn
are established. Under biased sampling models, the weighted empirical log-likelihood
ratio is shown to have an asymptotic scaled chi-square distribution for censored
data above mentioned. For the censored data whose usual nonparametric MLE are
of square-root rate of convergence, such as right censored data, doubly censored
data and partly interval-censored data, it is shown that 
weakly converges to a
centered Gaussian process, which leads to a consistent goodness of fit test for
the case-control logistic regression models. Some simulation results are presented.
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