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Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models. (English) Zbl 1169.62028
Summary: Empirical-likelihood-based inference for the nonparametric parts in semiparametric varying-coefficient partially linear (SVCPL) models is investigated. An empirical log-likelihood approach to construct the confidence regions/intervals of the nonparametric parts is developed. An estimated empirical likelihood ratio is proved to be asymptotically standard \(\chi ^{2}\)-limited. A simulation study indicates that, compared with a normal approximation based approach and the bootstrap method, the proposed method described herein works better in terms of coverage probabilities and average areas/widths of confidence regions/bands. An application to a real data set is illustrated.

MSC:
62G08 Nonparametric regression and quantile regression
62G15 Nonparametric tolerance and confidence regions
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62H12 Estimation in multivariate analysis
62E20 Asymptotic distribution theory in statistics
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