MULTIVARIATE LOCALLY WEIGHTED LEAST-SQUARES REGRESSION
MULTIVARIATE LOCALLY WEIGHTED LEAST-SQUARES REGRESSION
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DOI：
10.1214/aos/1176325632
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发表时间：
1994-09-01
影响因子：
4.5
通讯作者：
WAND, MP
中科院分区：
文献类型：
--
作者：
RUPPERT, D;WAND, MP
使用局部加权最小二乘的非参数回归是由Stone和Cleveland首先讨论的。最近，Fan以及Fan和Gijbels证明了局部线性核加权最小二乘回归估计量具有渐近性质，使其在某种意义上优于Nadaraya-Watson和Gasser-Muller核估计量。本文将渐近偏差和方差的结果推广到多元预测变量的情况。我们能够利用加权最小二乘矩阵理论推导出一般多变量核权的先导偏置项和方差项。这种方法在分析估计量的渐近条件偏差和方差时特别方便。我们还研究了Cleveland和Devlin讨论的多元局部二次最小二乘回归估计的渐近性质，并在单变量情况下，研究了高阶多项式拟合和导数估计。
Nonparametric regression using locally weighted least squares was first discussed by Stone and by Cleveland. Recently, it was shown by Fan and by Fan and Gijbels that the local linear kernel-weighted least squares regression estimator has asymptotic properties making it superior, in certain senses, to the Nadaraya-Watson and Gasser-Muller kernel estimators. In this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables. We are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory. This approach is especially convenient when analyzing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors. We also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by Cleveland and Devlin and, in the univariate case, higher-order polynomial fits and derivative estimation.