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Matrix differential calculus with applications in the multivariate linear model and its diagnostics

Author

Listed:
  • Liu, Shuangzhe
  • Leiva, Víctor
  • Zhuang, Dan
  • Ma, Tiefeng
  • Figueroa-Zúñiga, Jorge I.

Abstract

Matrix differential calculus is a powerful mathematical tool in multivariate analysis and related areas such as econometrics, environmetrics, geostatistics, predictive modeling, psychometrics, and statistics in general. One of the key contributions to its development was the introduction of the differential approach, which has led to a significant number of applications. In this paper, we present a study of this approach to matrix differential calculus with some of its key results along with illustrative examples. We also present new applications of this approach in the multivariate linear model: namely in efficiency comparisons, sensitivity analysis, and local influence diagnostics.

Suggested Citation

  • Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21001275
    DOI: 10.1016/j.jmva.2021.104849
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    References listed on IDEAS

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