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Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

Einbeck, Jochen (2003). Multivariate Local Fitting with General Basis Functions. Computational Statistics 18(2): 185-203.

Author(s) from Durham

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.