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

Ren, Jian-Jian

Ann. Statist., Tome 36 (2008) no. 1, p. 147-166 / Harvested from Project Euclid

Résumé

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 (θ̃_n, F̃_n) for the underlying parameter θ₀ and distribution F₀ is derived, and the strong consistency of (θ̃_n, F̃_n) and the asymptotic normality of θ̃_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.

Détail

Publié le : 2008-02-15
Classification:  Biased sampling,  bootstrap,  case-control data,  doubly censored data,  empirical likelihood,  Kolmogorov–Smirnov statistic,  interval censored data,  likelihood ratio,  logistic regression,  maximum likelihood estimator,  partly interval-censored data,  right censored data,  62N02,  62N03,  62N01