Testing lack of fit in multiple regression
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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. 2000 Biometrika Trust.