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Entropy 2016, 18(12), 421; doi:10.3390/e18120421

The Information Geometry of Sparse Goodness-of-Fit Testing

1
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
2
School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, Buckinghamshire MK7 6AA, UK
3
Department of Mathematics & ECARES, Université libre de Bruxelles, Avenue F.D. Roosevelt 42, 1050 Brussels, Belgium
*
Author to whom correspondence should be addressed.
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Received: 31 August 2016 / Revised: 16 November 2016 / Accepted: 19 November 2016 / Published: 24 November 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
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Abstract

This paper takes an information-geometric approach to the challenging issue of goodness-of-fit testing in the high dimensional, low sample size context where—potentially—boundary effects dominate. The main contributions of this paper are threefold: first, we present and prove two new theorems on the behaviour of commonly used test statistics in this context; second, we investigate—in the novel environment of the extended multinomial model—the links between information geometry-based divergences and standard goodness-of-fit statistics, allowing us to formalise relationships which have been missing in the literature; finally, we use simulation studies to validate and illustrate our theoretical results and to explore currently open research questions about the way that discretisation effects can dominate sampling distributions near the boundary. Novelly accommodating these discretisation effects contrasts sharply with the essentially continuous approach of skewness and other corrections flowing from standard higher-order asymptotic analysis. View Full-Text
Keywords: extended multinomial models; goodness-of-fit testing; information geometry extended multinomial models; goodness-of-fit testing; information geometry
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Marriott, P.; Sabolová, R.; Van Bever, G.; Critchley, F. The Information Geometry of Sparse Goodness-of-Fit Testing. Entropy 2016, 18, 421.

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