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

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.

### MSC:

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

Fahrmeir
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### References:

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