Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound
Hirofumi Wakaki, Vladimir V. Ulyanov · Theory of Probability and Its Applications · 2024
We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.