The distribution of Pearson residuals in generalized linear models

Details The distribution of Pearson residuals in generalized linear models The distribution of Pearson residuals in generalized linear models

2008-09-10

arxiv.org/abs/0809.1856v1

Computational Statistics & Data Analysis v. 53, p. 3397-3411, 2009.

Statistics

Methodology

Scientific paper

10.1016/j.csda.2009.02.025

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected Pearson residuals.

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