Density expansions for correlations and eigenvalues of the covariance matrix
Keywords:skew normal distribution, multivariate density expansion, multivariate cumulants, multivariate Hermite polynomials
In the paper explicit approximation formulae for the sample correlation coefficient and eigenvalues of the sample covariance matrix are found. The approximations are based on univariate and multivariate normal and skew normal distributions. A simulation experiment has been carried out where the empirical distributions are compared with different approximations.