TY - JOUR
T1 - Null distribution of the sum of squared z-transforms in testing complete independence
AU - Chen, Shande
AU - Mudholkar, Govind S.
PY - 1990/3/1
Y1 - 1990/3/1
N2 - Brien et al. (1984, Biometrika, 71, 545-554; 1988, Biometrika, 75, 469-476) have proposed, illustrated and discussed advantages of using Fisher's z-transforms for analyzing correlation structures of multinormal data. Chen and Mudholkar (1988, Austral. J. Statist., 31, 105-110) have studied the sum of squared z-transforms of sample correlations as a test statistic for complete independence. In this paper Brown's (1987, Ann. Probab., 15, 416-422) graph-theoretic characterization of the dependence structure of sample correlations is used to evaluate moments of the test statistic. These moments are then used to approximate its null distribution accurately over a broad range of parameters, including the case where the population dimension exceeds the sample size.
AB - Brien et al. (1984, Biometrika, 71, 545-554; 1988, Biometrika, 75, 469-476) have proposed, illustrated and discussed advantages of using Fisher's z-transforms for analyzing correlation structures of multinormal data. Chen and Mudholkar (1988, Austral. J. Statist., 31, 105-110) have studied the sum of squared z-transforms of sample correlations as a test statistic for complete independence. In this paper Brown's (1987, Ann. Probab., 15, 416-422) graph-theoretic characterization of the dependence structure of sample correlations is used to evaluate moments of the test statistic. These moments are then used to approximate its null distribution accurately over a broad range of parameters, including the case where the population dimension exceeds the sample size.
KW - Approximation
KW - correlation analysis
KW - dependence among sample correlations
UR - http://www.scopus.com/inward/record.url?scp=27944461390&partnerID=8YFLogxK
U2 - 10.1007/BF00050785
DO - 10.1007/BF00050785
M3 - Article
AN - SCOPUS:27944461390
VL - 42
SP - 149
EP - 155
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
SN - 0020-3157
IS - 1
ER -