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In this article, the weighted empirical likelihood is applied to a generalsetting of two-sample semiparametric models, which includes biased samplingmodels and case-control logistic regression models as special cases. Forvarious types of censored data, such as right censored data, doubly censoreddata, interval censored data and partly interval-censored data, the weightedempirical likelihood-based semiparametric maximum likelihood estimator$(\tilde{\theta}_n,\tilde{F}_n)$ for the underlying parameter $\theta_0$ anddistribution $F_0$ 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 weightedempirical log-likelihood ratio is shown to have an asymptotic scaledchi-squared distribution for censored data aforementioned. For right censoreddata, 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 logisticregression models.

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