IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.11052.html
   My bibliography  Save this paper

Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting

Author

Listed:
  • Mark Levene
  • Aleksejus Kononovicius

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 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 (${\cal E}SJS$) 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.

Suggested Citation

  • Mark Levene & Aleksejus Kononovicius, 2018. "Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting," Papers 1809.11052, arXiv.org, revised Jun 2019.
  • Handle: RePEc:arx:papers:1809.11052
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.11052
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Trevor Fenner & Mark Levene & George Loizou, 2018. "A multiplicative process for generating the rank-order distribution of UK election results," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(3), pages 1069-1079, May.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.
    5. Aleksejus Kononovicius, 2017. "Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections," Complexity, Hindawi, vol. 2017, pages 1-15, November.
    6. Nadarajah, Saralees & Kotz, Samuel, 2007. "On the q-type distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 465-468.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aleksejus Kononovicius & Bronislovas Kaulakys, 2022. "$1/f$ noise from the sequence of nonoverlapping rectangular pulses," Papers 2210.11792, arXiv.org, revised Mar 2023.
    2. Levene, Mark & Fenner, Trevor, 2021. "A stochastic differential equation approach to the analysis of the 2017 and 2019 UK general election polls," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1227-1234.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Katahira, Kei & Chen, Yu & Akiyama, Eizo, 2021. "Self-organized Speculation Game for the spontaneous emergence of financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Kei Katahira & Yu Chen, 2019. "Heterogeneous wealth distribution, round-trip trading and the emergence of volatility clustering in Speculation Game," Papers 1909.03185, arXiv.org.
    3. Jain, Prachi & Maitra, Debasish, 2023. "Risk implications of dependence in the commodities: A copula-based analysis," Global Finance Journal, Elsevier, vol. 57(C).
    4. Wang, Yudong & Wu, Chongfeng & Yang, Li, 2016. "Forecasting crude oil market volatility: A Markov switching multifractal volatility approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 1-9.
    5. Karoline Bax & Ozge Sahin & Claudia Czado & Sandra Paterlini, 2021. "ESG, Risk, and (Tail) Dependence," Papers 2105.07248, arXiv.org, revised Nov 2021.
    6. Su, Xiaoshan & Li, Yuhan, 2024. "Robust portfolio selection with subjective risk aversion under dependence uncertainty," Economic Modelling, Elsevier, vol. 132(C).
    7. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
    8. Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    9. Peter Neary & Monika MrázováMathieu Parenti, 2015. "Technology, Demand, And The Size Distribution Of Firms," Economics Series Working Papers 774, University of Oxford, Department of Economics.
    10. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    11. Zhiyuan Pan & Yudong Wang & Li Liu & Qing Wang, 2019. "Improving volatility prediction and option valuation using VIX information: A volatility spillover GARCH model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 744-776, June.
    12. Katahira, Kei & Chen, Yu & Hashimoto, Gaku & Okuda, Hiroshi, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 503-518.
    13. Fabrice Gilles & Sabina Issehnane & Florent Sari, 2022. "Using short-term jobs as a way to find a regular job. What kind of role for local context?," TEPP Working Paper 2022-07, TEPP.
    14. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang K., 2014. "TVICA—Time varying independent component analysis and its application to financial data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 95-109.
    15. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    16. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
    17. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    18. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    19. Juan C. Henao-Londono & Sebastian M. Krause & Thomas Guhr, 2021. "Price response functions and spread impact in correlated financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-20, April.
    20. Cornelia Lawson, 2013. "Academic Inventions Outside the University: Investigating Patent Ownership in the UK," Industry and Innovation, Taylor & Francis Journals, vol. 20(5), pages 385-398, July.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1809.11052. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.