An EM algorithm for estimating the parameters of the multivariate skew-normal distribution with censored responses

• Published in: Metron (Rome) 2022, Vol.80 (2), p.231-253
• Main Authors: Galarza, Christian E., Matos, Larissa A., Lachos, Victor H.
• Format: Article
• Language: English
• Subjects: Algorithms; Design of experiments; Error analysis; Inference; Mathematics and Statistics; Maximum likelihood estimation; Multivariate analysis; Normal distribution; Random errors; Regression models; Skewed distributions; Statistical analysis; Statistical Theory and Methods; Statistics
• ISSN: 0026-1424; 2281-695X
• DOI: 10.1007/s40300-021-00227-4

Limited or censored data are collected in many studies. This occurs for many reasons in several practical situations, such as limitations in measuring equipment or from an experimental design. Consequently, the true value is recorded only if it falls within an interval range so that the responses can be either left, interval, or right-censored. Missing values can be seen just as a particular case. Linear and nonlinear regression models are routinely used to analyze these types of data. Most of these models are based on the normality assumption for the error term. However, such analyses might not provide robust inference when the normality assumption (or symmetry) is questionable. The need for asymmetric distributions for the random errors motivates us to develop a likelihood-based inference for linear models with censored responses based on the multivariate skew-normal distribution, where the missing/censoring mechanism is assumed to be “missing at random” (MAR). The proposed EM-type algorithm for maximum likelihood estimation uses closed-form expressions at the E-step based on formulas for the mean and variance of a truncated multivariate skew-normal distribution, available in the R package MomTrunc . Three datasets with censored and/or missing observations are analyzed and discussed.