Abstract
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 \(\chi ^2\) 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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The authors acknowledge with gratitude the support of EPSRC grant EP/L010429/1.
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Marriott, P., Sabolova, R., Van Bever, G., Critchley, F. (2015). Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling . In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_61
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DOI: https://doi.org/10.1007/978-3-319-25040-3_61
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