  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.
