Abstract
Summary The first three approximate conditional moments of Pearson's goodness-of-fit statistic are derived for arbitrary linear exponential family models. The approximation is for large degrees of freedom and the conditioning variable is the sufficient statistic for the regression parameters. It is shown that when the data are sparse, the conditional variance can vary over several orders of magnitude, depending on the value of the conditioning variable. A simple algorithm involving a supplementary regression is described for computing the conditional moments, and Edgeworth approximation is suggested for the computation of significance levels.
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