标题： 带有各种类型截尾数据的一些两样本半参数模型的加权经验似然 显示英文标题

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

摘要： 本文中，加权经验似然方法被应用于两样本半参数模型的一般情形，该情形包含了偏抽样模型和病例对照逻辑回归模型作为特例。 对于各种类型的删失数据，如右删失数据、双重删失数据、区间删失数据以及部分区间删失数据，基于加权经验似然的半参数最大似然估计量$(\tilde{\theta}_n,\tilde{F}_n)$对潜在参数$\theta_0$和分布$F_0$进行推导，并且建立了估计量$(\tilde{\theta}_n,\tilde{F}_n)$的强相合性以及$\tilde{\theta}_n$的渐近正态性。 在偏抽样模型下，对于上述提及的删失数据，加权经验对数似然比被证明具有渐近尺度卡方分布。 对于右删失数据、双重删失数据以及部分区间删失数据，证明了$\sqrt{n}(\tilde{F}_n-F_0)$弱收敛到一个中心化的高斯过程，从而为病例对照逻辑回归模型提供了一致的良好性拟合检验。 显示英文摘要

摘要： 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.