Professor Heinz Neudecker and matrix differential calculus

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

Published in

Statistical Papers
2024, volume: 65, number: 4, pages: 2605–2639
Publisher: SPRINGER

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    
  • Linköping University

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1007/s00362-023-01499-w

Permanent link to this page (URI)

https://res.slu.se/id/publ/126569