Publication details for Jochen EinbeckEinbeck, Jochen (2004). Local fitting with a power basis. REVSTAT- Statistical Journal 2(2): 102-126.
- Publication type: Journal Article
- ISSN/ISBN: 1645-6726
- Keywords: local polynomial fitting, Taylor expansion, power basis, bias reduction
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.