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Contributions to Multivariate Analysis Due to C. R. Rao and Associated Developments

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Methodology and Applications of Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

C. R. Rao has made various significant contributions to multivariate analysis. Among them, we consider the following topics: (i) Rao’s U-statistic in discriminant analysis, (ii) MANOVA tests, (iii) Asymptotic expansion and Rao’s F approximation for \(\Lambda \) statistic, (iv) Growth curve analysis, and (v) Information criteria for the selection of variables. Some of these were introduced at the dawn of multivariate analysis. Under topic (v), we also discuss recent developments on the selection of variables in discriminant analysis.

Abbreviated title: Contributions to Multivariate Analysis due to Rao

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Acknowledgements

We would like to thank the two referees and Dr. K. P. Choi for their careful reading of our manuscript and many helpful comments which improved the presentation of this paper. Our thanks also go to the owner of Copyright in Elsevier for permission to reproduce a part of the foreword of Multivariate Analysis IV (P. R. Krishnaiah, ed., 1977, North-Holland Publishing Company) as in the first part of Sect. 6.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi Hiroshima, Hiroshima, 739-8626, Japan

    Yasunori Fujikoshi

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  1. Yasunori Fujikoshi
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Correspondence to Yasunori Fujikoshi .

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Editors and Affiliations

  1. Department of Statistics, University of California, Riverside, CA, USA

    Barry C. Arnold

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Narayanaswamy Balakrishnan

  3. NOVA School of Science and Technology, NOVA University of Lisbon, Caparica, Portugal

    Carlos A. Coelho

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Fujikoshi, Y. (2021). Contributions to Multivariate Analysis Due to C. R. Rao and Associated Developments. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_11

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