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On Tests for Equicorrelation Coefficient of a Standard Symmetric Multivariate Normal Distribution
Author(s) -
SenGufta Ashis
Publication year - 1987
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1987.tb00720.x
Subject(s) - mathematics , statistics , null distribution , z test , estimator , test statistic , multivariate normal distribution , normal distribution , statistic , bias of an estimator , statistical hypothesis testing , null hypothesis , likelihood ratio test
Summary Sampson (1976, 1978) has considered applications of the standard symmetric multivariate normal (SSMN) distribution and the estimation of its equi‐correlation coefficient, ρ. Tests for ρ are considered here. The likelihood ratio test suffers from several theoretical and practical shortcomings. We propose the locally most powerful (LMP) test which is globally (one‐sided) unbiased, very simple to compute and is based on the best natural unbiased estimator of ρ. Exact null and non‐null distributions of the test statistic are presented and percentage points are given. Statistical curvature (Efron, 1975) indicates that its performance improves with mk (sample size × dimension) while exact power computations show that even for reasonably small values of mk the performance is quite encouraging. Recalling Brown's (1971) cautions we establish by local comparison with the LMP similar test for ρ in the SMN (Rao, 1973) distribution, that here the additional information on the mean and variance is quite worthwhile.