Multivariate statistics and its applications

Abstract

Multivariate statistics and its applications have received more and more attention since 1950s.Multivariate statistical research in China was initiated by Pao-Lu Hsu duringthe end of 1930s and the beginning of 1940s in the so-called “Southwest United University”.Modern big data analysis makes classical multivariate statistical theory unable to accurately andeffectively solve practical problems. The theory of generalized multivariate statistics has beendeveloping very fast since 1970s. This paper aims to introduce the summary contributions that Chinesescholars have made in the development of generalized multivariate statistics and its applications inseveral aspects: (1) multivariate statistics and generalized multivariate statistics; (2) general symmetricmultivariate distributions; and (3) growth curve modeling and miscellaneous directions.Generalized multivariate statistics is an extension to the traditional statistics under the normalassumption. It aims to generalize the traditional statistical methodologies like parametric estimation,hypothesis testing, and modeling to a much wider family of multivariate distributionsthat are called elliptically contoured distributions (ECDs). General symmetric multivariate distributionsform an even wider class of multivariate probability distributions that includes the ECDs as its special case.Growth curve modeling (GCM) includes statistical methods that allow for consideration of inter-individualvariability in intra-individual patterns of chance over time. Outlier detection and identification ofinfluential observations are important topics in the area of GCM.