On new robust tests for the multivariate normal mean vector with high-dimensional data and applications

Abstract

New alternative tests to the Hotelling T2 and the likelihood ratio tests for the multivariate normal and non-normal population mean vector are proposed here. These new tests are based on the ordinary and robust comedian covariance matrix estimator. The new adapted likelihood ratio test overcomes the high dimensional issue that occurs with both T2 and likelihood ratio tests. The asymptotic and parametric bootstrap distributions for test statistics are used and the performance of these new tests based on normal and non-normal distributions is evaluated through Monte Carlo simulations. Contaminated normal multivariate populations are also considered to evaluate the eects of outliers on test performances. Type I error probabilities and power in all simulations are computed using the R software. The non-robust parametric bootstrap version of the likelihood ratio test performs better and is recommended since it is easy to implement and computationally fast. An application of the proposed new and T2 tests to a real data set is provided. We use an R package of our authorship to perform the tests described here.