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A note on computing maximum likelihood estimates for the three-parameter asymmetric Laplace distribution

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  • Wright, Stephen E.

Abstract

A finite-step procedure is proposed for maximum likelihood estimation of the three-parameter asymmetric Laplace distribution. Its performance is compared with the iterative method most commonly used for this distribution. The new procedure is much faster and reliably identifies samples for which maximum likelihood estimates lie on the boundary of the parameter space, making it a good choice for simulation studies and simulation-based methodologies.

Suggested Citation

  • Wright, Stephen E., 2024. "A note on computing maximum likelihood estimates for the three-parameter asymmetric Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    • Handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005507
    DOI: 10.1016/j.amc.2023.128381
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    References listed on IDEAS

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    1. Samuel Kotz & Tomasz Kozubowski & Krzysztof Podgórski, 2002. "Maximum Likelihood Estimation of Asymmetric Laplace Parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 816-826, December.
    2. Hinkley, David V. & Revankar, Nagesh S., 1977. "Estimation of the Pareto law from underreported data : A further analysis," Journal of Econometrics, Elsevier, vol. 5(1), pages 1-11, January.
    3. William McGill, 1962. "Random fluctuations of response rate," Psychometrika, Springer;The Psychometric Society, vol. 27(1), pages 3-17, March.
    4. Geraci, Marco, 2014. "Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i13).
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