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Professor Heinz Neudecker and matrix differential calculus

Author

Listed:
  • Shuangzhe Liu

    (University of Canberra)

  • Götz Trenkler

    (Dortmund University of Technology)

  • Tõnu Kollo

    (University of Tartu)

  • Dietrich Rosen

    (Swedish University of Agricultural Sciences
    Linköping University)

  • Oskar Maria Baksalary

    (Adam Mickiewicz University)

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.

Suggested Citation

  • Shuangzhe Liu & Götz Trenkler & Tõnu Kollo & Dietrich Rosen & Oskar Maria Baksalary, 2024. "Professor Heinz Neudecker and matrix differential calculus," Statistical Papers, Springer, vol. 65(4), pages 2605-2639, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01499-w
    DOI: 10.1007/s00362-023-01499-w
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