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Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

Einbeck, Jochen (2004). Local fitting with a power basis. REVSTAT- Statistical Journal 2(2): 102-126.

Author(s) from Durham

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.