Asymptotic expansion in reduced rank regression under normality and nonnormality

Asymptotic expansions of the distributions of the parameter estimators in reduced rank regression are obtained under arbitrary distributions. As an asymptotic expansion, Hall's method with variable transformation is shown as well as the results by the Edgeworth and Cornish-Fisher expansions. In the model for standardized variables, the Wishart maximum likelihood estimators of parameters are derived with the corresponding asymptotic expansions. Robust properties of some asymptotic cumulants of the parameter estimators for unstandardized variables are given. Numerical examples show advantages of the asymptotic expansions over the usual normal approximation. The method of adaptation to the case of model misspecification is also provided.