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Local fitting with a power basis

Einbeck, Jochen

Authors



Abstract

Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method to a simulated data set for various basis functions and discuss situations where the fit can be improved by using a suitable basis. Finally, some remarks about bandwidth selection are given and the method is applied to real data.

Citation

Einbeck, J. (2004). Local fitting with a power basis. Revstat Statistical Journal, 2(2), 102-126

Journal Article Type Article
Publication Date Nov 1, 2004
Deposit Date Nov 13, 2009
Journal Revstat Statistical Journal
Print ISSN 1645-6726
Publisher Instituto Nacional de Estatística
Peer Reviewed Peer Reviewed
Volume 2
Issue 2
Pages 102-126
Keywords Local polynomial fitting, Taylor expansion, Power basis, Bias reduction.
Publisher URL http://www.ine.pt/revstat/autores/JEinbeck.html


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