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Walking on the Road to the Statistical Pyramid

–Prof. Kai-Tai Fang’s Contribution to Multivariate Statistics

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Contemporary Experimental Design, Multivariate Analysis and Data Mining

Abstract

This paper reviews Prof. Kai-Tai Fang’s major contribution to multivariate statistics in three aspects: generalized multivariate statistics; general symmetric multivariate distributions; growth curve models and miscellaneous fields. Generalized multivariate statistics is a large extension of traditional statistics with normal assumption. It aims to generalize the traditional statistical methodologies like parametric estimation, hypothesis testing, and modeling to a much wider family of multivariate distributions, which is called elliptically contoured distributions (ECD). General symmetric multivariate distributions form an even wider class of multivariate probability distributions that includes the ECD as its special case. Growth curve models (GCM) includes statistical methods that allow for consideration of inter-individual variability in intra-individual patterns of change over time. Outlier detection and identification of influential observations are important topics in the area of the GCM. Miscellaneous fields cover major contributions that Prof. Fang made in various areas of multivariate statistics beyond the three aspects mentioned above.

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Authors and Affiliations

  1. University of Manchester, Manchester, UK

    Jianxin Pan

  2. University of New Haven, West Haven, USA

    Jiajuan Liang

  3. Southern University of Science and Technology, Shenzhen, China

    Guoliang Tian

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  1. Jianxin Pan
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  2. Jiajuan Liang
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Correspondence to Jiajuan Liang .

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Editors and Affiliations

  1. Department of Financial Engineering, Princeton University, Princeton, NJ, USA

    Jianqing Fan

  2. Department of Mathematics, The University of Manchester, Manchester, UK

    Jianxin Pan

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Pan, J., Liang, J., Tian, G. (2020). Walking on the Road to the Statistical Pyramid. In: Fan, J., Pan, J. (eds) Contemporary Experimental Design, Multivariate Analysis and Data Mining. Springer, Cham. https://doi.org/10.1007/978-3-030-46161-4_1

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