Preprint No.
A-98-16
Rainer Schwabe, Ewaryst Rafajlowicz
Experimental Design for (Semi-)Local Regression
Abstract: Our aim is to discuss a new problem statement of
experimental design, which is applicable when
a regression model is not completely specified.
The starting
point to the proposed approach is the local regression model,
for which local experiments are considered.
Then, the notion of a local design extendability
under a family of transformations
is introduced and basic properties of extendable
designs are established. Extendable designs allow for
an exploratory analysis of adjacent domains, retaining
part of the observations gained earlier.
Under some technical assumptions it is also proved that
if a locally D-optimal experiment design is saturated and extendable
to adjacent regions, then it is also D-optimal when it is considered
globally, i.e. in the whole area covered by local experiments.
The results of the paper are formulated for the
D-optimality criterion,
but the main points of the proposed approach can be generalized to
other design optimality criteria.
Keywords: experimental design, exploratory regression analysis,
partly specified models
Mathematics Subject Classification (MSC91): 62K05 Optimal designs
, 62G07 Curve estimation (nonparametric regression, density estimation, etc.)
Language: ENG
Available: Pr-A-98-16.ps
Contact: Schwabe, Rainer; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (schwabe@math.fu-berlin.de)
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