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.
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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 |
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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 Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
Research Centres and Institutes: | Data Analytics, Birkbeck Institute for |
Depositing User: | Administrator |
Date Deposited: | 04 Jun 2019 09:03 |
Last Modified: | 09 Aug 2023 12:46 |
URI: | https://eprints.bbk.ac.uk/id/eprint/27719 |
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