Heteroscedastic and heavy-tailed regression with mixtures of skew Laplace normal distributions

ABSTRACT

Joint modelling skewness and heterogeneity is challenging in data analysis, particularly in regression analysis which allows a random probability distribution to change flexibly with covariates. This paper, based on a skew Laplace normal (SLN) mixture of location, scale, and skewness, introduces a new regression model which provides a flexible modelling of location, scale and skewness parameters simultaneously. The maximum likelihood (ML) estimators of all parameters of the proposed model via the expectation-maximization (EM) algorithm as well as their asymptotic properties are derived. Numerical analyses via a simulation study and a real data example are used to illustrate the performance of the proposed model.

KEYWORDS:

• EM algorithm
• joint location, scale and skewness models
• mixture model
• ML estimation
• SLN
• SN

Acknowledgments

This study is supported by ‘The Scientific and Technological Research Council of Turkey (TUBITAK)’ (grant number: 1059B191700233) as part of ‘2219-International Postdoctoral Research Scholarship Programme’. This research was conducted when the first author visited Brunel University London. The authors would like to thank the university which hosted the visit. Finally, the authors thank two anonymous referees and the associate editor for their thoughtful suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Fatma Zehra Doğru http://orcid.org/0000-0001-8220-2375

Keming Yu http://orcid.org/0000-0001-6341-8402

Olcay Arslan http://orcid.org/0000-0002-7067-4997

Additional information

Funding

This study is supported by ‘The Scientific and Technological Research Council of Turkey (TUBITAK)’ (grant number 1059B191700233) as part of ‘2219-International Postdoctoral Research Scholarship Programme’.