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Entropy, Vol. 20, Pages 464: Non-Quadratic Distances in Model Assessment

Entropy, Vol. 20, Pages 464: Non-Quadratic Distances in Model Assessment

Entropy doi: 10.3390/e20060464

Authors: Marianthi Markatou Yang Chen

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.

Authors:   Markatou, Marianthi ; Chen, Yang
Journal:   Entropy
Volume:   20
edition:   6
Year:   2018
Pages:   464
DOI:   10.3390/e20060464
Publication date:   14-Jun-2018
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