A NONPARAMETRIC REGRESSION ESTIMATOR THAT ADAPTS TO ERROR DISTRIBUTION OF UNKNOWN FORM
A NONPARAMETRIC REGRESSION ESTIMATOR THAT ADAPTS TO ERROR DISTRIBUTION OF UNKNOWN FORM
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DOI：
10.1017/s026646660707017x
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发表时间：
2001-06
影响因子：
0.8
通讯作者：
O. Linton;Zhijie Xiao
中科院分区：
文献类型：
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作者：
O. Linton;Zhijie Xiao
对于误差分布未知的非参数回归，提出了一种新的核估计。我们证明了所提出的估计量是自适应的，因为它渐近等价于不可行的局部似然估计量（Staniswalis，1989，Journal of the American Statistical Association 84，276-283; Fan，Farmen，and Gijbels，1998，Journal of the皇家统计学会，系列B 60，591-608;和Fan和Chen，1999，Journal of the皇家统计学会，系列B 61，927-943），其需要误差分布的知识。因此，当误差分布不正态时，我们的估计改进了标准的非参数核估计。我们进行了一个Monte Carlo实验来研究我们的方法在有限样本下的性能。我们感谢Yuichi Kitamura，Yanqin Fan，Joel Horowitz，Roger Koenker，Jens Perch Nielsen，Peter菲利普斯，Peter罗宾逊，Tom Rothenberg和两位裁判的有益评论。感谢NSF和ESRC（英国）的财政支持。
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 (Staniswalis, 1989, Journal of the American Statistical Association 84, 276–283; Fan, Farmen, and Gijbels, 1998, Journal of the Royal Statistical Society, Series B 60, 591–608; and Fan and Chen, 1999, Journal of the Royal Statistical Society, Series B 61, 927–943), 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.We thank Yuichi Kitamura, Yanqin Fan, Joel Horowitz, Roger Koenker, Jens Perch Nielsen, Peter Phillips, Peter Robinson, Tom Rothenberg, and two referees for helpful comments. Financial support from the NSF and the ESRC (UK) is gratefully acknowledged.