Model checks for generalized linear models. (English) Zbl 1035.62073

Stute, Winfried; Zhu, Li-Xing

Scand. J. Stat. 29, No. 3, 535-545 (2002).

For a generalized regression model \(E(Y\,|\, X=x)=m (\beta^T_0 x, \vartheta_0)\) (\(m\) being a link function, \(\beta_0\), \(\vartheta_0\) are unknown parameters) a test is proposed for the correctness of link function specification. It is based on the residual cusum process projected onto the \(\beta_n\) direction (\(\beta_n\) is some estimator for \(\beta_0\)). Convergence of this process to a Gaussian limit is demonstrated. An innovation process transform is proposed to derive a statistic which is asymptotically distribution free. Results of simulations are presented.

Reviewer: R. E. Maiboroda (Kyïv)

MSC:

62J12	Generalized linear models (logistic models)
62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference

Keywords:

generalized linear regression; asymptotically distribution free statistics; residual cusum process

Software:

Fahrmeir

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