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
From these we select such sequences,
which assure the best possible
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,
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
Contact: Schwabe, Rainer; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (firstname.lastname@example.org)
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