A likelihood-ratio-based normal approximation for the non-null distribution of the multiple correlation coefficient
作者:
Panagis G. Moschopoulos,
Govind S. Mudholkar,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1983)
卷期:
Volume 12,
issue 3
页码: 355-371
ISSN:0361-0918
年代: 1983
DOI:10.1080/03610918308812323
出版商: Marcel Dekker, Inc.
关键词: hypergeometric functions;asymptotic expansions;cumulants of multiple correlation;Wilson and Hilferty transformation
数据来源: Taylor
摘要:
Let X1,X2, …, Xpbe jointly distributed according to a multivariate normal distribution, and let ? denote the multiple correlation coefficient between X1and X2, X3,…, XpLet Xli,…, Xpi, i =1, … N, be a random sample from the distribution. The logarithm of the likelihood ratio statistic for testing the hypothesis that ρ is zero is −(N/2)log(l−R2), where R is the sample multiple correlation coefficient. A Gaussian approximation to the non-null (ρ≠0) distribution of R is developed using the transformation (T/E(T))hwhere T =−log(l−R2), and h is determined from the first three cumulants of T. The approximation is simple and accurate over a wide range of the parameters p, N, and ρ.
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