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October 1998 Model checks for regression: an innovation process approach
Winfried Stute, Silke Thies, Li-Xing Zhu
Ann. Statist. 26(5): 1916-1934 (October 1998). DOI: 10.1214/aos/1024691363


In the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus, smooth and directional goodness-of-fit tests. Since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain, we propose to replace this process by its innovation martingale. It turns out that the resulting tests are (asymptotically) distribution free under composite null models and may be readily performed. A simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes.


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Winfried Stute. Silke Thies. Li-Xing Zhu. "Model checks for regression: an innovation process approach." Ann. Statist. 26 (5) 1916 - 1934, October 1998.


Published: October 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0930.62044
MathSciNet: MR1673284
Digital Object Identifier: 10.1214/aos/1024691363

Primary: 62G30 60G44
Secondary: 62G10

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 5 • October 1998
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