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

Shuangzhe Liu, Víctor Leiva, Dan Zhuang, Tiefeng Ma and Jorge I. Figueroa-Zúñiga

Journal of Multivariate Analysis, 2022, vol. 188, issue C

Abstract: 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.

Keywords: Hessian; Jacobian; Kantorovich inequality; Least squares method; Matrix derivative; Maximum likelihood method; Sensitivity analysis; Statistical diagnostics (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2021.104849

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