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Weighted empirical likelihood in some two-sample semiparametric models with various types of censored data. (English) Zbl 1132.62083

Summary: 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 \((\widetilde \theta _n, \widetilde F _n)\) for the underlying parameter \(\theta _{0}\) and distribution \(F_{0}\) is derived, and the strong consistency of \((\widetilde \theta _n, \widetilde F_n)\) and the asymptotic normality of \(\widetilde \theta _n\) 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 \(\sqrt n (\widetilde F _n - F_0)\) weakly converges to a centered Gaussian process, which leads to a consistent goodness-of-fit test for the case-control logistic regression models.

MSC:

62N01 Censored data models
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62N02 Estimation in survival analysis and censored data
62N03 Testing in survival analysis and censored data
62G05 Nonparametric estimation
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