| Abstract | In this study we develop two near-exact distributions for the generalized Wilks Lambda statistic, used to test the independence of several sets of variables, with multivariate normal distribution, for the case where two or more sets have an odd number of variables. Using the concept of near-exact distributions and based on a factorization of the exact characteristic function we obtain two approximations, which are very close to the exact distribution but far more manageable. These near-exact distributions equate, by construction, some of the first exact moments and they correspond to cumulative distribution functions which are practical to use, allowing for an easy computation of near-exact quantiles. We also develop three asymptotic distributions which also equate some of the first exact moments. We assess the proximity of the asymptotic and near-exact distributions obtained to the exact distribution using two measures based on the Berry-Esseen bounds. In this comparative numerical study we consider different numbers of sets of variables, different numbers of variables per set and different sample sizes. |
