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.
PY - 2023/10/3
Y1 - 2023/10/3
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
SP - 1
EP - 35
JO - Statistical Papers
JF - Statistical Papers
ER -