A constrained maximum likelihood estimation for skew normal mixtures

Libin Jin, Sung Nok Chiu, Jianhua Zhao, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


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.
Original languageEnglish
Pages (from-to)391–419
Number of pages29
Issue number4
Early online date30 Jun 2022
Publication statusPublished - May 2023

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Boundary estimator
  • Constraint maximum likelihood estimator
  • Likelihood degeneracy
  • Skew normal mixtures
  • Strong consistency


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