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Asyptotic Normality for Maximum Likelihood Estimation and Operational Risk

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  • Paul Larsen

Abstract

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how asymptotic normality does--or does not--hold for common severity distributions in operational risk models. We then apply these results to evaluate errors caused by failure of asymptotic normality in constructing confidence intervals around the MLE fitted parameters.

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  • Paul Larsen, 2015. "Asyptotic Normality for Maximum Likelihood Estimation and Operational Risk," Papers 1508.02824, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1508.02824
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    References listed on IDEAS

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    1. Patrick de Fontnouvelle & Eric Rosengren & John Jordan, 2007. "Implications of Alternative Operational Risk Modeling Techniques," NBER Chapters, in: The Risks of Financial Institutions, pages 475-505, National Bureau of Economic Research, Inc.
    2. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-424, July.
    3. Brazauskas, Vytaras, 2002. "Fisher information matrix for the Feller-Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 159-167, September.
    4. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
    5. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
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    Cited by:

    1. Jung, Yongsu & Lee, Ikjin, 2021. "Optimal design of experiments for optimization-based model calibration using Fisher information matrix," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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