A skew factor analysis model based on the normal mean-variance mixture of Birnbaum-Saunders distribution

Farzane Hashemi; Mehrdad Naderi; Ahad Jamalizadeh; Tsung-I Lin

doi:10.1080/02664763.2019.1709054

A skew factor analysis model based on the normal mean-variance mixture of Birnbaum-Saunders distribution

J Appl Stat. 2020 Jan 6;47(16):3007-3029. doi: 10.1080/02664763.2019.1709054. eCollection 2020.

Authors

Farzane Hashemi^{1

2}, Mehrdad Naderi², Ahad Jamalizadeh¹, Tsung-I Lin^{3

4}

Affiliations

¹ Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
² Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa.
³ Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.
⁴ Department of Public Health, China Medical University, Taichung, Taiwan.

Abstract

This paper presents a robust extension of factor analysis model by assuming the multivariate normal mean-variance mixture of Birnbaum-Saunders distribution for the unobservable factors and errors. A computationally analytical EM-based algorithm is developed to find maximum likelihood estimates of the parameters. The asymptotic standard errors of parameter estimates are derived under an information-based paradigm. Numerical merits of the proposed methodology are illustrated using both simulated and real datasets.

Keywords: Birnbaum–Saunders distribution; EM algorithm; factor analysis; outliers; skewness.

Grants and funding

This work is partially supported by the National Research Foundation, South Africa (reference: CPRR160403161466, grant number 105840, SARChI Research Chair – UID: 71199, and STATOMET) and the Ministry of Science and Technology of Taiwan [grant number 107-2118-M-005-002-MY2].