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Modified Wald statistics for generalized linear models
Authors:Andreas Oelerich and Thorsten Poddig
Institution:(1) Lehrstuhl für Finanzwirtschaft, Universität Bremen, 28359 Bremen
Abstract:Summary: Wald statistics in generalized linear models are asymptotically KHgr2 distributed. The asymptotic chi–squared law of the corresponding quadratic form shows disadvantages with respect to the approximation of the finite–sample distribution. It is shown by means of a comprehensive simulation study that improvements can be achieved by applying simple finite–sample size approximations to the distribution of the quadratic form in generalized linear models. These approximations are based on a KHgr2 distribution with an estimated degree of freedom that generalizes an approach by Patnaik and Pearson. Simulation studies confirm that nominal level is maintained with higher accuracy compared to the Wald statistics.
Keywords:Chi–  square approximation  generalized linear models  hypothesis testing  quadratic forms  logistic regression  small sample size
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