The Annals of Statistics

Model checks for regression: an innovation process approach

Winfried Stute, Silke Thies, and Li-Xing Zhu

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Abstract

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.

Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1916-1934.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691363

Digital Object Identifier
doi:10.1214/aos/1024691363

Mathematical Reviews number (MathSciNet)
MR1673284

Zentralblatt MATH identifier
0930.62044

Subjects
Primary: 62G30 60G44
Secondary: 62G10: Hypothesis testing

Keywords
Residual cusum process innovation process goodness-of-fit tests

Citation

Stute, Winfried; Thies, Silke; Zhu, Li-Xing. Model checks for regression: an innovation process approach. Ann. Statist. 26 (1998), no. 5, 1916--1934. doi:10.1214/aos/1024691363. https://projecteuclid.org/euclid.aos/1024691363


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