A nonparametric version of Wilks' lambda--Asymptotic results and small sample approximations

We propose a nonparametric version of Wilks' lambda (the multivariate likelihood ratio test) and investigate its asymptotic properties under the two different scenarios of either large sample size or large number of samples. For unbalanced samples, a weighted and an unweighted variant are introduced. The unweighted variant of the proposed test appears to be novel also in the normal-theory context. The theoretical results are supplemented by a simulation study with parameter settings that are motivated by clinical and agricultural data, considering in particular the performance for small sample sizes, small number of samples, and varying dimensions. Inference methods based on the asymptotic sampling distribution and a small sample approximation are compared to permutation tests and to other parametric and nonparametric procedures. Application of the proposed method is illustrated by examples.