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Biometrika 2000 87(2):405-424; doi:10.1093/biomet/87.2.405
© 2000 by Biometrika Trust
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Testing lack of fit in multiple regression

M AertsA1, G ClaeskensA2 and JD HartA3

A1 Centre for Statistics, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium E-mail: marc.aerts@luc.ac.be A2 Department of Statistics, Eindhoven University of Technology, Den Dolech 2, PO box 513, NL-5600 MB Eindhoven, The Netherlands E-mail: g.a.m.claeskens@tue.nl A3 Department of Statistics, Texas A&M University, College Station, TX 77843, USA E-mail: hart@stat.tamu.edu

We study lack-of-fit tests based on orthogonal series estimators. A common feature of these tests is that they are functions of score statistics that employ data-driven model dimensions. The criteria used to select the dimension are score-based versions of AIC and BIC. The tests can be applied in a wide variety of settings, including both continuous and discrete data. With two or more covariates, a model sequence, i.e. a path in the alternative models space, has to be chosen. Critical points and p-values of the lack-of-fit tests can be obtained via asymptotic distribution theory or by use of the bootstrap. Data examples and a simulation study illustrate the applicability of the tests.

Key Words: additive model; lack of fit; multiple regression; nonparametric series estimation; omnibus test; penalised score; score statistic


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