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Empirical likelihood for generalized linear models with missing responses. (English) Zbl 1209.62054

Summary: The paper uses the empirical likelihood method to study the construction of confidence intervals and regions for regression coefficients and response mean in generalized linear models with missing response. By using the inverse selection probability weighted imputation technique, the proposed empirical likelihood ratios are asymptotically chi-squared. Our approach is to directly calibrate the empirical likelihood ratio, which is called as a bias-correction method. Also, a class of estimators for the parameters of interest is constructed, and the asymptotic distributions of the proposed estimators are obtained. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths/areas of confidence intervals/regions. An example of a real data set is used for illustrating our methods.

MSC:

62G05 Nonparametric estimation
62J12 Generalized linear models (logistic models)
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)
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