Professor Heinz Neudecker and matrix differential calculus

Shuangzhe Liu (), Götz Trenkler (), Tõnu Kollo (), Dietrich Rosen () and Oskar Maria Baksalary ()
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Shuangzhe Liu: University of Canberra
Götz Trenkler: Dortmund University of Technology
Tõnu Kollo: University of Tartu
Dietrich Rosen: Swedish University of Agricultural Sciences
Oskar Maria Baksalary: Adam Mickiewicz University

Statistical Papers, 2024, vol. 65, issue 4, No 26, 2605-2639

Abstract: Abstract 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.

Keywords: Matrix differential calculus; Random matrix; Statistical moment; Asymptotic distribution; Efficiency comparison; Multivariate linear model (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01499-w

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