On some Diagonalized and Regularized Hotelling's T^2 Tests of Location for High Dimensional Data

Olusola MAKİNDE, Odunayo OMOTOSO
2020 GAZI UNIVERSITY JOURNAL OF SCIENCE  
Highlights • A revisit to the diagonalized and regularized Hotelling's 2 tests. • Notions of data depth for trimming of mean vectors and covariance matrices. • Comparison of diagonalized and regularized Hotelling's 2 tests with the usual Hotelling's 2 test. • Limitations of diagonalized and regularized Hotelling's 2 tests in high dimension. • Proposal of robust versions of diagonalized and regularized Hotelling's 2 tests in high dimension. Article Info Abstract A widely used statistical test of
more » ... statistical test of hypothesis for location parameter in ℝ is the Hotelling's 2 test. This test is efficient if data is normally distributed, ratio of sample size to dimension diverges and there are no outliers in the data. However, it is practically impossible to implement when dimension is greater than sample size. As a remedial measure, diagonalized and regularized Hotelling's 2 tests were proposed. In this paper, powers of regularized and diagonalized Hotelling's 2 tests are compared with the usual Hotelling's 2 test in low dimension and the usual Hotelling's 2 perform much better. It is observed that diagonalized Hotelling's 2 test may have low power for mixture distributions. Due to a comparative performance of regularized and diagonalized Hotelling's 2 tests, robust versions of diagonalized and regularized Hotelling's 2 tests are proposed in high dimension in the presence of outliers. The powers of these tests were compared using simulated as well as real datasets.
doi:10.35378/gujs.642062 fatcat:qc7qx25lqffatjcjfhvigajcru