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Entropy 2018, 20(6), 464; https://doi.org/10.3390/e20060464

Non-Quadratic Distances in Model Assessment

Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA
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Received: 31 March 2018 / Revised: 11 June 2018 / Accepted: 13 June 2018 / Published: 14 June 2018
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Abstract

One natural way to measure model adequacy is by using statistical distances as loss functions. A related fundamental question is how to construct loss functions that are scientifically and statistically meaningful. In this paper, we investigate non-quadratic distances and their role in assessing the adequacy of a model and/or ability to perform model selection. We first present the definition of a statistical distance and its associated properties. Three popular distances, total variation, the mixture index of fit and the Kullback-Leibler distance, are studied in detail, with the aim of understanding their properties and potential interpretations that can offer insight into their performance as measures of model misspecification. A small simulation study exemplifies the performance of these measures and their application to different scientific fields is briefly discussed. View Full-Text
Keywords: model assessment; statistical distance; non-quadratic distance; total variation; mixture index of fit; Kullback-Leibler distance; divergence measure model assessment; statistical distance; non-quadratic distance; total variation; mixture index of fit; Kullback-Leibler distance; divergence measure
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Markatou, M.; Chen, Y. Non-Quadratic Distances in Model Assessment. Entropy 2018, 20, 464.

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