NDLI: On maximum likelihood estimation of a Pareto mixture

Content Provider	Springer Nature Link
Author	Bee, Marco Benedetti, Roberto Espa, Giuseppe
Copyright Year	2011
Abstract	In this paper we deal with maximum likelihood estimation (MLE) of the parameters of a Pareto mixture. Standard MLE procedures are difficult to apply in this setup, because the distributions of the observations do not have common support. We study the properties of the estimators under different hypotheses; in particular, we show that, when all the parameters are unknown, the estimators can be found maximizing the profile likelihood function. Then we turn to the computational aspects of the problem, and develop three alternative procedures: an EM-type algorithm, a Simulated Annealing and an algorithm based on Cross-Entropy minimization. The work is motivated by an application in the operational risk measurement field: we fit a Pareto mixture to operational losses recorded by a bank in two different business lines. Under the assumption that each population follows a Pareto distribution, the appropriate model is a mixture of Pareto distributions where all the parameters have to be estimated.
Starting Page	161
Ending Page	178
Page Count	18
File Format	PDF
ISSN	09434062
Journal	Computational Statistics
Volume Number	28
Issue Number	1
e-ISSN	16139658
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-11-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Pareto distribution Finite mixture Simulated annealing Cross-entropy Profile likelihood Operational risk Statistics Probability and Statistics in Computer Science Probability Theory and Stochastic Processes Economic Theory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty Computational Mathematics

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