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Empirical likelihood inference for the parameter in additive partially linear EV models. (English) Zbl 1202.62045
Summary: We consider empirical likelihood inference for the parameters in additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distributed without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct a confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.
MSC:
62G05Nonparametric estimation
62G15Nonparametric tolerance and confidence regions
62G20Nonparametric asymptotic efficiency
62J02General nonlinear regression
62E20Asymptotic distribution theory in statistics
65C60Computational problems in statistics