Local fitting with a power basis

Einbeck, Jochen

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
• Electronic ISSN: 2183-0371
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1547323
• Publisher URL: http://www.ine.pt/revstat/autores/JEinbeck.html