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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