TY - JOUR
T1 - A generalized Shapiro-Wilk W statistic for testing high-dimensional normality
AU - Liang, Jiajuan
AU - TANG, Man Lai
AU - Chan, Ping Shing
N1 - Funding Information:
This work was supported by a grant from the Hong Kong Baptist University (project number FRG/07-08/II-35), and a University of New Haven 2008 Summer Research Grant.
PY - 2009/9/1
Y1 - 2009/9/1
N2 - Shapiro and Wilk's [Shapiro, S.S., Wilk, M.B., 1965. An analysis of variance test for normality (complete samples). Biometrika 52, 591-611] W-statistic was found to have competitive power performance in testing univariate normality. Generalizations of the W-statistic to the multivariate case have been proposed by many researchers. In this paper, we propose a family of generalized W-statistics for testing high-dimensional normality by using the theory of spherical distributions. The proposed statistics apply to the case that the sample size is smaller than the dimension. Monte Carlo studies demonstrate feasible performance of the proposed tests in controlling type I error rates and power against some non-normal data. It is concluded that the proposed statistics are superior to existing generalizedW-statistics and show competitive benefits in testing high-dimensional normality with small sample size.
AB - Shapiro and Wilk's [Shapiro, S.S., Wilk, M.B., 1965. An analysis of variance test for normality (complete samples). Biometrika 52, 591-611] W-statistic was found to have competitive power performance in testing univariate normality. Generalizations of the W-statistic to the multivariate case have been proposed by many researchers. In this paper, we propose a family of generalized W-statistics for testing high-dimensional normality by using the theory of spherical distributions. The proposed statistics apply to the case that the sample size is smaller than the dimension. Monte Carlo studies demonstrate feasible performance of the proposed tests in controlling type I error rates and power against some non-normal data. It is concluded that the proposed statistics are superior to existing generalizedW-statistics and show competitive benefits in testing high-dimensional normality with small sample size.
UR - http://www.scopus.com/inward/record.url?scp=66049116306&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2009.04.016
DO - 10.1016/j.csda.2009.04.016
M3 - Journal article
AN - SCOPUS:66049116306
SN - 0167-9473
VL - 53
SP - 3883
EP - 3891
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 11
ER -