An EM algorithm for fitting matrix-variate normal distributions on interval-censored and missing data

• Published in: Statistics and computing Vol. 35; no. 2
• Main Authors: Lachos, Victor H., Tomarchio, Salvatore D., Punzo, Antonio, Ingrassia, Salvatore
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2025; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computer Science; Datasets; Maximum likelihood estimation; Missing data; Normal distribution; Original Paper; Parameter estimation; Probability and Statistics in Computer Science; Spatiotemporal data; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Water quality; Censored data; Missing data; ECM algorithm; Truncated moments; Matrix-variate distribution
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-025-10575-0

Matrix-variate distributions are powerful tools for modeling three-way datasets that often arise in longitudinal and multidimensional spatio-temporal studies. However, observations in these datasets can be missing or subject to some detection limits because of the restriction of the experimental apparatus. Here, we develop an efficient EM-type algorithm for maximum likelihood estimation of parameters, in the context of interval-censored and/or missing data, utilizing the matrix-variate normal distribution. This algorithm provides closed-form expressions that rely on truncated moments, offering a reliable approach to parameter estimation under these conditions. Results obtained from the analysis of both simulated data and real case studies concerning water quality monitoring are reported to demonstrate the effectiveness of the proposed method.