Likelihood-based inference for the multivariate skew-t regression with censored or missing responses

• Published in: Journal of multivariate analysis Vol. 196; p. 105174
• Main Authors: Valeriano, Katherine A.L., Galarza, Christian E., Matos, Larissa A., Lachos, Victor H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2023
• Subjects: Censored data; EM algorithm; Extended skew-[formula omitted] distribution; Missing observations; Truncated distributions; secondary; Censored data; Truncated distributions; Extended skew-t distribution; EM algorithm; Missing observations; primary
• DOI: 10.1016/j.jmva.2023.105174
• ISSN: 0047-259X

Skew-t regression models have been widely used to model and analyze asymmetric heavy-tailed data. Moreover, observations in this kind of data can be missing or subject to some upper and/or lower detection limits because of the restriction of the experimental apparatus. We propose a novel robust regression model for multiple censored or missing data based on the multivariate skew-t distribution for such data structures. This approach allows us to model data with great flexibility, simultaneously accommodating heavy tails and skewness. We develop an analytically simple yet efficient EM-type algorithm to conduct maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated multivariate Student’s-t, skew-t, and extended skew-t distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method.