
Abstract
We propose goodness of fit tests for testing generalized linear models and semiparametric regression models against smooth alternatives. The focus is on models having both, continuous and factorial covariates. As smooth extension of a parametric or semiparametric model we use generalized varying coefficient models as proposed by Hastie&Tibshirani (JRSS B, 1993). A likelihood ratio statistic is used for testing, and asymptotic normality of the test statistic is proven. Due to a slow asymptotic convergence rate a bootstrap approach is pursued. Asymptotic expansions allow to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping. The test is shown to have sqrt(n) power, but in contrast to parametric tests it is powerful against smooth alternatives in general.
Item Type: | Paper |
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Keywords: | Likelihood Ratio, Local Likelihood Fitting, Model Checking, Semiparametric Models, Smoothing |
Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |
Subjects: | 500 Science > 510 Mathematics |
URN: | urn:nbn:de:bvb:19-epub-1538-3 |
Language: | English |
Item ID: | 1538 |
Date Deposited: | 04. Apr 2007 |
Last Modified: | 04. Nov 2020, 12:45 |