A constrained maximum likelihood estimation for skew normal mixtures

Libin Jin, Sung Nok Chiu, Jianhua Zhao and Lixing Zhu ()
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Libin Jin: Shanghai Lixin University of Accounting and Finance
Sung Nok Chiu: Hong Kong Baptist University
Jianhua Zhao: Yunnan University of Finance and Economics
Lixing Zhu: Hong Kong Baptist University

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 4, No 1, 419 pages

Abstract: Abstract For a finite mixture of skew normal distributions, the maximum likelihood estimator is not well-defined because of the unboundedness of the likelihood function when scale parameters go to zero and the divergency of the skewness parameter estimates. To overcome these two problems simultaneously, we propose constrained maximum likelihood estimators under constraints on both the scale parameters and the skewness parameters. The proposed estimators are consistent and asymptotically efficient under relaxed constraints on the scale and skewness parameters. Numerical simulations show that in finite sample cases the proposed estimators outperform the ordinary maximum likelihood estimators. Two real datasets are used to illustrate the success of the proposed approach.

Keywords: Skew normal mixtures; Likelihood degeneracy; Boundary estimator; Constraint maximum likelihood estimator; Strong consistency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00873-2

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