TY - JOUR
T1 - Professor Heinz Neudecker and matrix differential calculus
AU - Liu, Shuangzhe
AU - Trenkler, Götz
AU - Kollo, Tõnu
AU - von Rosen, Dietrich
AU - Baksalary, Oskar Maria
N1 - Funding Information:
Tönu Kollo acknowledges support from the Estonian Research Foundation (Grant Number PRG1197).
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Funding Information:
We express our gratitude to Professor Heinz Neudecker\u2019s children, Ilia, Hannah and Franz, for providing us with relevant documents and publications, as well as for reading and approving the manuscript. We also extend our appreciation to the Editors and Reviewers for their constructive comments and insights, which significantly contributed to the improved presentation of the manuscript. We would like to thank the following individuals for their valuable communications and support over the years: Drs. Peter Boswijk, Richard William Farebrother, Jan Hauke, Emiel Kaper, Augustyn Markiewicz, Stephen Pollock, Simo Puntanen, Willem Saris, Albert Satorra, George Styan, Sven-Oliver Troschke, Michel van de Velden, Tom Wansbeek, and Frank Windmeijer. Special thanks go to Drs. Ejaz Ahmed, Jorge Figueroa-Z\u00FA\u00F1iga, Stephen Haslett, Xiaogang Huang, Jun Jin, Kazuhiko Kakamu, Takeaki Kariya, Victor Leiva, Hang Liu, Lin Ma, Tiefeng Ma, Gilberto Paula, Jianmei Ren, Ruili Sun, Yoshio Takane, Qijing Yan, Hu Yang, Xiaoping Zhan and Dan Zhuang for their joint efforts and collaborations. We would also like to acknowledge the useful feedback and support received from Drs. Kai-Tai Fang, Chengcheng Hao, Jianhua Hu, Jeffrey Hunter, Lynn Roy LaMotte, Rui Li, Yuli Liang, Hui Liu, Yonghui Liu, Changyu Lu, Seng Huat Ong, Jianxin Pan, Lei Shi, Kunio Shimizu, Martin Singull, Yongge Tian, Kimmo Vehkalahti, Julia Volaufova, Hongxing Wang, Fuzhen Zhang, Shurong Zheng, Fukang Zhu, and other participants during the talk based on partial materials of this manuscript, which was presented at the 27th International Workshop on Matrices and Statistics, IWMS-2019, held at Shanghai University of International Business and Economics, China on 6\u20139 June 2019. Finally, we would like to pay tribute to the late Drs. Risto Heijmans, Wolfgang Polasek, and Haruo Yanai, whose dedication to their colleagues and students continues to inspire us. Though they are no longer with us, their legacy lives on.
Funding Information:
T\u00F6nu Kollo acknowledges support from the Estonian Research Foundation (Grant Number PRG1197).
Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
PY - 2024/6
Y1 - 2024/6
N2 - The late Professor Heinz Neudecker (1933–2017) made significant contributions to the development of matrix differential calculus and its applications to econometrics, psychometrics, statistics, and other areas. In this paper, we present an insightful overview of matrix-oriented findings and their consequential implications in statistics, drawn from a careful selection of works either authored by Professor Neudecker himself or closely aligned with his scientific pursuits. The topics covered include matrix derivatives, vectorisation operators, special matrices, matrix products, inequalities, generalised inverses, moments and asymptotics, and efficiency comparisons within the realm of multivariate linear modelling. Based on the contributions of Professor Neudecker, several results related to matrix derivatives, statistical moments and the multivariate linear model, which can literally be considered to be his top three areas of research enthusiasm, are particularly included.
AB - The late Professor Heinz Neudecker (1933–2017) made significant contributions to the development of matrix differential calculus and its applications to econometrics, psychometrics, statistics, and other areas. In this paper, we present an insightful overview of matrix-oriented findings and their consequential implications in statistics, drawn from a careful selection of works either authored by Professor Neudecker himself or closely aligned with his scientific pursuits. The topics covered include matrix derivatives, vectorisation operators, special matrices, matrix products, inequalities, generalised inverses, moments and asymptotics, and efficiency comparisons within the realm of multivariate linear modelling. Based on the contributions of Professor Neudecker, several results related to matrix derivatives, statistical moments and the multivariate linear model, which can literally be considered to be his top three areas of research enthusiasm, are particularly included.
KW - Asymptotic distribution
KW - Efficiency comparison
KW - Matrix differential calculus
KW - Multivariate linear model
KW - Random matrix
KW - Statistical moment
UR - http://www.scopus.com/inward/record.url?scp=85173085449&partnerID=8YFLogxK
U2 - 10.1007/s00362-023-01499-w
DO - 10.1007/s00362-023-01499-w
M3 - Other Journal Article
AN - SCOPUS:85173085449
SN - 0932-5026
VL - 65
SP - 2605
EP - 2639
JO - Statistical Papers
JF - Statistical Papers
IS - 4
ER -