Premium
Testing generalized linear and semiparametric models against smooth alternatives
Author(s) -
Kauermann Göran,
Tutz Gerhard
Publication year - 2001
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00281
Subject(s) - semiparametric model , mathematics , semiparametric regression , parametric statistics , covariate , bootstrapping (finance) , test statistic , generalized linear model , goodness of fit , statistic , linear model , contrast (vision) , likelihood ratio test , parametric model , statistical hypothesis testing , statistics , econometrics , computer science , artificial intelligence
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 continous and factorial covariates. As a smooth extension of a parametric or semiparametric model we use generalized varying‐coefficient models as proposed by Hastie and Tibshirani. A likelihood ratio statistic is used for testing. Asymptotic expansions allow us to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping of the test statistic. The test is shown to have √ n ‐power, but in contrast with parametric tests it is powerful against smooth alternatives in general.