Preprint No. A-98-12

Rainer Schwabe, Ewaryst Rafajlowicz

The Performance of Equidistributed Sequences in Nonparametric Regression Based on a Quasi Least Squares Method

Abstract: In this paper a method of generating experimental designs for estimating a response function is proposed. This method is based on results for multivariate integration by means of quasi Monte Carlo methods. We start with sequences of (deterministic) uniformly distributed points. From these we select such sequences, which assure the best possible convergence rate of a quasi least squares nonparametric regression function estimator (in the integrated mean squared error sense). Such sequences can be generated by vectors for which the components are algebraically independent. Finally, in the class of those vectors we search for generators, which are well suited already for estimation by a moderate number of observations. The proposed design sequences are not necessarily optimal in the classical sense, which requires a model to be completely specified, but useful when the model is not completely specified and various sets of model spanning functions are to be considered.

Mathematics Subject Classification (MSC91): 62J02 General nonlinear regression , 62K05 Optimal designs

Language: ENG


Contact: Schwabe, Rainer; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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