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Multivariate local fitting with general basis functions.

Einbeck, J. (2003) 'Multivariate local fitting with general basis functions.', Computational statistics., 18 (2). pp. 185-203.

Abstract

In this paper we combine the concepts of local smoothing and fitting with basis functions for multivariate predictor variables. We start with arbitrary basis functions and show that the asymptotic variance at interior points is independent of the choice of the basis. Moreover we calculate the asymptotic variance at boundary points. We are not able to compute the asymptotic bias since a Taylor theorem for arbitrary basis functions does not exist. For this reason we focus on basis functions without interactions and derive a Taylor theorem which covers this case. This theorem enables us to calculate the asymptotic bias for interior as well as for boundary points. We demonstrate how advantage can be taken of the idea of local fitting with general basis functions by means of a simulated data set, and also provide a data-driven tool to optimize the basis.

Item Type:Article
Keywords:Bias reduction, Local polynomial fitting, Multivariate kernel smoothing, Taylor expansion.
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1007/s001800300140
Record Created:20 Mar 2008
Last Modified:23 Sep 2014 13:39

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