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 χ2 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.
CITATION STYLE
Marriott, P., Sabolova, R., van Bever, G., & Critchley, F. (2015). Geometry of goodness-of-fit testing in high dimensional low sample size modelling. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 569–576). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_61
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