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Empirical likelihood-based inferences for generalized partially linear models. (English) Zbl 1197.62092

A generalized linear model is considered for the response \(Y\), where \[ E(Y| X,T)=\mu(X'\beta +\vartheta(T)),\quad \text{Var}(Y| X,T)=\sigma^2 V(\mu), \] where \(\mu\) and \(V\) are known functions, \(X\) are regressors, \(T\) are covariates and \(\vartheta\) is an unknown function. An empirical likelihood ratio based on the quasi-likelihood function \[ Q(\mu,y)=\int_\mu^y (s-y)/V(s)ds \] is considered. Convergence of the empirical likelihood ratio to the \(\chi^2\) distribution is demonstrated. Confidence regions for \(\beta\) are constructed. Results of simulations and an application to AIDS data are presented.

MSC:

62J12 Generalized linear models (logistic models)
62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G15 Nonparametric tolerance and confidence regions
65C60 Computational problems in statistics (MSC2010)
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