TY - JOUR
T1 - A characterization of multivariate normal distribution and its application
AU - Yang, Zhen-Hai
AU - Fang, Kai-Tai
AU - Liang, Jia-Juan
N1 - Funding Information:
* Corresponding author. 1 This work was supported by Hong Kong UGC grant, the Statistics Research and Consultancy Unit, HKBU and the NSF of China and the NSF of Beijing.
PY - 1996/11/15
Y1 - 1996/11/15
N2 - Let X1, X2, ⋯ ,Xn be i.i.d. d-dimensional random vectors with a continuous density. Let Sk = ∑ki = 1 XiXTi, Yk = Sk-1/2Xk and Zk = Yk/(√1 - YTk Yk) (k ≥ d). In this paper we find that the distribution of Zk (or Yk) can be used for characterizing multivariate normal distribution. This characterization can be employed for testing multivariate normality in terms of the so-called transformation method.
AB - Let X1, X2, ⋯ ,Xn be i.i.d. d-dimensional random vectors with a continuous density. Let Sk = ∑ki = 1 XiXTi, Yk = Sk-1/2Xk and Zk = Yk/(√1 - YTk Yk) (k ≥ d). In this paper we find that the distribution of Zk (or Yk) can be used for characterizing multivariate normal distribution. This characterization can be employed for testing multivariate normality in terms of the so-called transformation method.
KW - Characterization of multinormality
KW - Multivariate normal distribution
KW - Spherical distribution
UR - http://www.scopus.com/inward/record.url?scp=0030588768&partnerID=8YFLogxK
U2 - 10.1016/S0167-7152(95)00238-3
DO - 10.1016/S0167-7152(95)00238-3
M3 - Journal article
AN - SCOPUS:0030588768
SN - 0167-7152
VL - 30
SP - 347
EP - 352
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 4
ER -