Matrix differential calculus with applications in the multivariate linear model and its diagnostics

Matrix differential calculus is a powerful mathematical tool in multivariate analysis and related areas such as econometrics, environmetrics, geostatistics, predictive modeling, psychometrics, and statistics in general. One of the key contributions to its development was the introduction of the differential approach, which has led to a significant number of applications. In this paper, we present a study of this approach to matrix differential calculus with some of its key results along with illustrative examples. We also present new applications of this approach in the multivariate linear model: namely in efficiency comparisons, sensitivity analysis, and local influence diagnostics. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

Matrix differential calculus is a powerful mathematical tool widely used in multivariate analysis and related fields. The introduction of the differential approach has significantly contributed to its development and led to numerous applications. This paper presents a study of the matrix differential calculus approach, including key results and illustrative examples. It also introduces new applications of this approach in the multivariate linear model, such as efficiency comparisons, sensitivity analysis, and local influence diagnostics.