Validation of linear regression models
Dette, Holger ; Munk, Axel
Ann. Statist., Tome 26 (1998) no. 3, p. 778-800 / Harvested from Project Euclid
A new test is proposed in order to verify that a regression function, say $g$, has a prescribed (linear) parametric form. This procedure is based on the large sample behavior of an empirical $L^2$-distance between $g$ and the subspace $U$ spanned by the regression functions to be verified. The asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the $L^2$-distance between the regression function $g$ and the model space $U$. Based on this result, a test is proposed for the hypothesis that "$g$ is not in a preassigned $L^2$-neighborhood of $U$," whichallows the "verification" of the model $U$ at a controlled type I error rate. The suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic. In particular, it does not require nonparametric estimators of the regression function and hence, the test does not depend on the subjective choice of smoothing parameters.
Publié le : 1998-04-14
Classification:  Nonparametric model check,  validation of goodness of fit,  $L^2$-distance,  equivalence of regression functions,  62G05,  62G10,  62G30,  62G07
@article{1028144860,
     author = {Dette, Holger and Munk, Axel},
     title = {Validation of linear regression models},
     journal = {Ann. Statist.},
     volume = {26},
     number = {3},
     year = {1998},
     pages = { 778-800},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1028144860}
}
Dette, Holger; Munk, Axel. Validation of linear regression models. Ann. Statist., Tome 26 (1998) no. 3, pp.  778-800. http://gdmltest.u-ga.fr/item/1028144860/