Distribution and density approximation of the covariance matrix in the growth curve model

Approximations of the distribution for the maximum likelihood estimator of the dispersion matrix in the Growth Curve model due to Potthoff and Roy (19 64) are considered. Three different approaches are presented. Two are based on an Edgeworth type expansion where as approximating distribution two dif ferent Wishart distributions are used. In a third approach we utilize the s tructure of the estimator and combine an Edgeworth type expansion with an a pproach put forward by Fujikoshi (1985).