Non-Quadratic Distances in Model Assessment

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.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.