On the Densities of the Scale-Invariant Statistics of the Multiple and Partial Correlation Coefficients

Abstract

This work examines both the elliptically contoured Wishart density and the
resulting density of the total correlation coefficient, and reaffirms the invariance property of the squared sampled multiple correlation coefficient. This invariance property is then exploited to show that the densities of the multiple correlation coefficients for the standard normal model and for the elliptically contoured model are identical. The same is shown to also hold for the density of the partial correlation coefficients.

Keywords: Scale invariance, elliptically contoured model, multiple and partial correlation coefficients.