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

Marriott, Paul; Sabolova, Radka; Van Bever, Germain and Critchley, Frank (2015). Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling. In: Geometric Science of Information (Nielsen, Frank and Barbaresco, Frédéric eds.), Lecture Notes in Computer Science, Springer International Publishing, pp. 569–576.

DOI: https://doi.org/10.1007/978-3-319-25040-3_61

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 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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