A robust Likelihood Ratio Test for high-dimensional MANOVA -- with excellent performance

Abstract: The present paper answers the following questions related with high-dimensional manova: (i) is it possible to develop a likelihood ratio test for high-dimensional manova? (ii) would such test perform well? (iii) would it be able to outperform existing tests? (iv) would it be applicable to extremely small samples? (v) would it be applicable to non-normal random variables, as uniform, extremely skewed distributions, or even heavy tailed distributions with success? (vi) would it have a nice, rather simple to compute and well performing, asymptotic distribution? And what about if the answer to all the above questions would be a clear 'Yes'? Surprisingly enough, it is exactly the case. Extensive simulations, with both normal and non-normal distributions, some of which are heavy tailed and/or highly skewed, and even discrete distributions, are carried out in order to evaluate the performance of the proposed test and to compare its performance with other tests. Two real data applications are presented.