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 -