Generalized T3-plot for testing high-dimensional normality

doi:10.1007/s11464-016-0535-x

Front. Math. China

2016, Vol. 11

Issue (6) : 1363-1378 https://doi.org/10.1007/s11464-016-0535-x

RESEARCH ARTICLE

Generalized T₃-plot for testing high-dimensional normality

Mingyao AI^1,^*(

),Jiajuan LIANG²,Man-Lai TANG³

¹. LMAM, School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing 100871, China
². Department of Marketing, College of Business, University of New Haven, West Haven, CT 06516, USA
³. Department of Mathematics and Statistics, School of Business, Hang Seng Management College, Hong Kong, China

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Abstract

A new dimension-reduction graphical method for testing highdimensional normality is developed by using the theory of spherical distributions and the idea of principal component analysis. The dimension reduction is realized by projecting high-dimensional data onto some selected eigenvector directions. The asymptotic statistical independence of the plotting functions on the selected eigenvector directions provides the principle for the new plot. A departure from multivariate normality of the raw data could be captured by at least one plot on the selected eigenvector direction. Acceptance regions associated with the plots are provided to enhance interpretability of the plots. Monte Carlo studies and an illustrative example show that the proposed graphical method has competitive power performance and improves the existing graphical method significantly in testing high-dimensional normality.

Keywords Dimension reduction graphical method high-dimensional data multivariate normality spherical distribution

Corresponding Author(s): Mingyao AI

Issue Date: 18 October 2016

Cite this article:

Mingyao AI,Jiajuan LIANG,Man-Lai TANG. Generalized T₃-plot for testing high-dimensional normality[J]. Front. Math. China, 2016, 11(6): 1363-1378.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0535-x
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I6/1363

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