A goodness-of-fit test for parametric and semi-parametric models in multiresponse regression
Song Xi Chen and Ingrid Van Keilegom
Source: Bernoulli Volume 15, Number 4
(2009), 955-976.
Abstract
We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric models, like the multiindex and the partially linear models; and models with shape constraints. Another feature of the test is that it allows both the response variable and the covariate be multivariate, which means that multiple regression curves can be tested simultaneously. The test also allows the presence of infinite-dimensional nuisance functions in the model to be tested. It is shown that the empirical likelihood test statistic is asymptotically normally distributed under certain mild conditions and permits a wild bootstrap calibration. Despite the large size of the class of models to be considered, the empirical likelihood test enjoys good power properties against departures from a hypothesized model within the class.
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Keywords: additive regression; bootstrap; empirical likelihood; goodness of fit; infinite-dimensional parameter; kernel estimation; monotone regression; partially linear regression
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1262962222
Digital Object Identifier: doi:10.3150/09-BEJ208
Mathematical Reviews number (MathSciNet): MR2597579
Zentralblatt MATH identifier: 1200.62047
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