Edgeworth expansion of Wilks’ lambda statistic

An asymptotic expansion of the null distribution of the Wilks’ lambda statistic is derived when some of the parameters are large. Cornish–Fisher expansions of the upper percent points are also obtained. A monotone transformation which reduces the third and the fourth order cumulants is also derived. In order to study the accuracy of the approximation formulas, some numerical experiments are done, with comparing to the classical expansions when only the sample size tends to infinity.