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A nonparametric regression estimator that adapts to error distribution of unknown form. (English) Zbl 1274.62292
Summary: We propose a new kernel estimator for nonparametric regression with unknown error distribution. We show that the proposed estimator is adaptive in the sense that it is asymptotically equivalent to the infeasible local likelihood estimator [J. G. Staniswalis, J. Am. Stat. Assoc. 84, No. 405, 276–283 (1989; Zbl 0721.62039); J. Fan et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 60, No. 3, 591–608 (1998; Zbl 0909.62036); J. Fan and J. Chen, ibid. 61, No. 4, 927–943 (1999; Zbl 0940.62039)], which requires knowledge of the error distribution. Hence, our estimator improves on standard nonparametric kernel estimators when the error distribution is not normal. A Monte Carlo experiment is conducted to investigate the finite-sample performance of our procedure.

MSC:
62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
Software:
KernSmooth
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