Data sharpening methods in multivariate local quadratic regression

Xiaoying Wang, Song Jiang and Junping Yin

Journal of Multivariate Analysis, 2012, vol. 105, issue 1, 258-275

Abstract: This paper is concerned with the conditional bias and variance of local quadratic regression to the multivariate predictor variables. Data sharpening methods of nonparametric regression were first proposed by Choi, Hall, Roussion. Recently, a data sharpening estimator of local linear regression was discussed by Naito and Yoshizaki. In this paper, to improve mainly the fitting precision, we extend their results on the asymptotic bias and variance. Using the data sharpening estimator of multivariate local quadratic regression, we are able to derive higher fitting precision. In particular, our approach is simple to implement, since it has an explicit form, and is convenient when analyzing the asymptotic conditional bias and variance of the estimator at the interior and boundary points of the support of the density function.

Keywords: Data sharpening methods; Multivariate nonparametric regression; Local quadratic estimator; Asymptotic conditional bias and variance; Fitting precision; Bandwidth matrix (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.jmva.2011.09.004

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