Title: Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting,
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 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 we advocate herein, is to use a
nonparametric measure for model comparison between the raw data and the fitted
model. In particular, for this purpose we put forward the {\em Survival
Jensen-Shannon divergence} ($SJS$) and its empirical counterpart (${\cal
E}SJS$) 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 ${\cal E}SJS$, 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 of interest to researchers in
sociophysics and econophysics.