Asymptotic expansions for the distributions of functions of a correlation matrix

This paper deals with asymptotic expansions for the non-null distributions of certain test statistics concerning a correlation matrix in a multivariate normal distribution. For this purpose an asymptotic expansion is given for the distribution of a function of the sample correlation matrix. As special cases of the resulting expansion, asymptotic expansions for the distributions of the sample correlation coefficient, Fisher's z-transformation and arcsine transformation are also given.