A likelihood-ratio-based normal approximation for the non-null distribution of the multiple correlation coefficient
Titel:
A likelihood-ratio-based normal approximation for the non-null distribution of the multiple correlation coefficient
Auteur:
Moschopoulos, Panagis G. Mudholkar, Govind S.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 12 (1983) nr. 3 pagina's 355-371
Jaar:
1983
Inhoud:
Let X1,X2, …, Xp be jointly distributed according to a multivariate normal distribution, and let ? denote the multiple correlation coefficient between X1 and X2, X3,…, Xp Let 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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