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Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation

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  • Lu, Zhan-Qian
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    Abstract

    Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In this paper, we develop current work on locally weighted regression and generalize locally weighted polynomial fitting to the estimation of partial derivatives in a multivariate regression context. Specifically, for both the regression and partial derivative estimators we prove joint asymptotic normality and derive explicit asymptotic expansions for their conditional bias and conditional convariance matrix (given observations of predictor variables) in each of the two important cases of local linear fit and local quadratic fit.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 2 (November)
    Pages: 187-205

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:187-205

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    Keywords: locally weighted regression joint asymptotic normality asymptotic bias asymptotic variance kernel estimator nonparametric regression;

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    Cited by:
    1. Zhang, Wenyang & Lee, Sik-Yum, 2000. "Variable Bandwidth Selection in Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 116-134, July.
    2. Zhan-Qian Lu, 1999. "Multivariate Local Polynomial Fitting for Martingale Nonlinear Regression Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 51(4), pages 691-706, December.

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