Goodness-of-Fit Test for Generalized Linear Models

Gerhard Dikta () and Marsel Scheer
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Gerhard Dikta: FH Aachen – University of Applied Sciences, Department of Medical Engineering and Technomathemathics
Marsel Scheer: Bayer AG

Chapter Chapter 6 in Bootstrap Methods, 2021, pp 165-230 from Springer

Abstract: Abstract Goodness-of-fit (GOF) tests in regression analysis are mainly based on the observed residuals. In a series of articles, starting with Stute (1997), Stute established a general approach for GOF tests which is based on a marked empirical process (MEP), a standardized cumulative sum process obtained from the observed residuals. Resting upon the asymptotic limiting process of the MEP under the null hypothesis, Kolmogorov-Smirnov or Cramér-von Mises type tests can be stated as GOF tests. Their asymptotic distributions are derived through an application of the continuous mapping theorem. Since, in most cases, the asymptotic distributions depend on the model and, therefore, are not distribution free, further concepts are necessary to obtain the critical values for these tests.

Date: 2021
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DOI: 10.1007/978-3-030-73480-0_6

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