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An improved procedure for the estimation of a correlation matrix. (English) Zbl 0577.62050
Statistical theory and data analysis, Proc. 1st Pac. Area Stat. Conf., Tokyo 1982, 369-379 (1985).
[For the entire collection see Zbl 0564.00021.]
A procedure for obtaining an improved estimate of the population correlation matrix of an m-dimensional multivariate normal distribution, P, for small to moderate samples is presented in this paper. The approach is to transform (approximately) the problem of estimating P into that of estimating a multivariate normal mean vector by transforming the m(m-1)/2 sample correlations into the Fisher z-scale, and then applying a version of the James-Stein estimator to the transformed statistics.
The transformation is then inverted, yielding an estimate of the correlation matrix P. A simulation study is employed to compare the performance of the proposed estimator with the ML estimator.

MSC:
62H12 Estimation in multivariate analysis