Empirical survival Jensen-Shannon divergence as a goodness-of-fit measure for maximum likelihood estimation and curve fitting

Levene, Mark and Kononovicius, A. (2019) Empirical survival Jensen-Shannon divergence as a goodness-of-fit measure for maximum likelihood estimation and curve fitting. Communications in Statistics - Simulation and Computation 50 (11), pp. 3751-3767. ISSN 0361-0918.

Abstract

The coefficient of determination, known as R2, is commonly used as a goodness-of-fit criterion for fitting linear models. R2 is somewhat controversial when fitting nonlinear models, although it may be generalised 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 non- parametric measure for comparison between the empirical distribution, comprising the raw data, and the fitted model. In particular, for this purpose we put forward the Survi- val Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) as a metric which is bounded, and is a natural generalisation of the Jensen-Shannon divergence. We demonstrate, via a straightforward procedure making use of the ESJS, 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.

Metadata

Statistics

DownloadsShow export options

Export as XMLJSONCSV

Activity Overview

6 month trend

179Downloads

6 month trend

144Hits

Additional statistics are available via IRStats2.

Archive Staff Only (login required)

Edit/View Item