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Keywords:

  • generalized linear model;
  • goodness-of-fit;
  • innovation approach;
  • residual cusum process;
  • spherically contoured inputs

In this paper we propose and study non-parametric tests for the validity of (composite) Generalized Linear Models with a given parametric link structure, which are based on certain empirical processes marked by the residuals. When properly transformed to their innovation part the resulting test statistics are distribution-free. The method perfectly adapts to a situation, when also the input vector follows a dimension reducing model.