It is proved the algebraic equality between Jennrich's (1970) asymptotic $X^2$ test for equality of correlation matrices, and a Wald test statistic derived from Neudecker and Wesselman's (1990) expression of the asymptotic variance matrix of the sample correlation matrix.

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting and appropriate asymptotic variance matrix of sample moments. Scaled test...