TY - JOUR
T1 - Matrix differential calculus with applications in the multivariate linear model and its diagnostics
AU - Liu, Shuangzhe
AU - Leiva, Víctor
AU - Zhuang, Dan
AU - Ma, Tiefeng
AU - Figueroa-Zúñiga, Jorge I.
N1 - Funding Information:
We would like to sincerely thank the Editors, Professors Tõnu Kollo and Dietrich von Rosen, for their constructive and insightful comments which significantly benefitted our understanding of matrix derivatives as well as the presentation of this manuscript. The research of V. Leiva was partially supported by FONDECYT , project grant number 1200525 , from the National Agency for Research and Development (ANID) of the Chilean Government under the Ministry of Science, Technology, Knowledge and Innovation . The research of D. Zhuang was supported by the Education and Scientific Research Project Foundation of Young and Middle-Aged Teachers of Fujian Province , China (No. JAT190068 ).
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - Hessian
KW - Jacobian
KW - Kantorovich inequality
KW - Least squares method
KW - Matrix derivative
KW - Maximum likelihood method
KW - Sensitivity analysis
KW - Statistical diagnostics
UR - http://www.scopus.com/inward/record.url?scp=85118860304&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2021.104849
DO - 10.1016/j.jmva.2021.104849
M3 - Article
AN - SCOPUS:85118860304
SN - 1095-7243
VL - 188
SP - 1
EP - 13
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104849
ER -