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Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling


Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling
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We introduce a new approach to goodness-of-fit testing in the high dimensional, sparse extended multinomial context. The paper takes a computational information geometric approach, extending classical higher order asymptotic theory. We show why the Wald – equivalently, the Pearson X2 and score statistics – are unworkable in this context, but that the deviance has a simple, accurate and tractable sampling distribution even for moderate sample sizes. Issues of uniformity of asymptotic approximations across model space are discussed. A variety of important applications and extensions are noted.
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Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling
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