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    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 , ISSN 0361-0918. (In Press)

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    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

    Item Type: Article
    Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis, available online at the link above.
    Keyword(s) / Subject(s): divergence measures, goodness-of-fit, maximum likelihood, curve fitting, survival, Jensen-Shannon divergence
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Administrator
    Date Deposited: 04 Jun 2019 09:03
    Last Modified: 22 Aug 2019 01:29
    URI: http://eprints.bbk.ac.uk/id/eprint/27719

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