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Weighted empirical likelihood in some two-sample semiparametric models with various types of censored data
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DOI：10.1214/009053607000000695.png)
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Abstract
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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 ((theta) over tilde (n), (F) over tilde (n)) for the underlying parameter theta(0) and distribution F(0) is derived, and the strong consistency of ((theta) over tilde (n), (F) over tilde (n)) and the asymptotic normality of (theta) over tilde (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 root n((F) over tilde (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.
Keywords:
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
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