Empirical survival Jensen-Shannon divergence as a goodness-of-Fit measure for maximum likelihood estimation and curve fitting. Issue 11 (2nd November 2021)

• Record Type: Journal Article
• Authors: Levene, Mark; Kononovicius, Aleksejus
• Is Part Of: Communications in statistics. Volume 50:Issue 11(2021)
• Page Start: 3751
• Page End: 3767
• Publication Date: 2021-11-02
• Subjects: Divergence measures -- Goodness-of-fit -- Maximum likelihood -- Curve fitting -- Survival Jensen-Shannon divergence; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2019.1630435
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: The coefficient of determination, known as R 2, is commonly used as a goodness-of-fit criterion for fitting linear models. R 2 is somewhat controversial when fitting nonlinear models, although it may be generalized on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to a data set using, say, the maximum likelihood estimation method. A general approach to measure the goodness-of-fit of the fitted parameters, which is advocated herein, is to use a nonparametric measure for comparison between the empirical distribution, comprising the raw data, and the fitted model. In particular, for this purpose we put forward the Survival Jensen-Shannon divergence ( SJS ) and its empirical counterpart ( E SJS ) as a metric which is bounded, and is a natural generalization of the Jensen-Shannon divergence. We demonstrate, via a straightforward procedure making use of the E SJS, that it can be used as part of maximum likelihood estimation or curve fitting as a measure of goodness-of-fit, including the construction of a confidence interval for the fitted parametric distribution. Furthermore, we show the validity of the proposed method with simulated data, and three empirical data sets.