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Empirical likelihood for semiparametric varying-coefficient partially linear regression models. (English) Zbl 1086.62057
Summary: This paper is concerned with the estimation problem of the varying-coefficient partially linear regression model. We apply the empirical method to this semiparametric model. An empirical log-likelihood ratio for the parametric components, which are of primary interest, is proposed and a nonparametric version of Wilk’s theorem is derived. Thus, confidence regions of the parametric components with asymptotically correct coverage probabilities can be constructed.
Compared with those based on normal approximations, the confidence regions based on the empirical likelihood have two advantages: (1) they do not have the predetermined symmetry, which enables them to better correspond with the true shape of the underlying distribution; (2) they do not involve any asymptotic covariance matrix estimation and hence are robust against the heteroscedasticity. Some simulations and an application are conducted to illustrate the proposed method.

MSC:
62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62F25 Parametric tolerance and confidence regions
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