Testing lack of fit of regression models under heteroscedasticity
Author(s) -
Li ChinShang
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316106
Subject(s) - heteroscedasticity , nonparametric regression , mathematics , null hypothesis , parametric statistics , nonparametric statistics , null distribution , kernel regression
Abstract A test is proposed for assessing the lack of fit of heteroscedastic nonlinear regression models that is based on comparison of nonparametric kernel and parametric fits. A data‐driven method is proposed for bandwidth selection using the asymptotically optimal bandwidth of the parametric null model which leads to a test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The resulting test is applied to the problem of testing the lack of fit of a generalized linear model.