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

Abstract

A widely used statistical test of hypothesis for location parameter in R^p is the Hotelling’s T^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 T^2 tests were proposed. In this paper, powers of regularized and diagonalized Hotelling’s T^2 tests are compared with the usual Hotelling’s T^2 test in low dimension and the usual Hotelling’s T^2 perform much better. It is observed that diagonalized Hotelling’s T^2 test may have low power for mixture distributions. Due to a comparative performance of regularized and diagonalized Hotelling’s T^2 tests, robust versions of diagonalized and regularized Hotelling’s T^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.

Keywords

• High-dimensional data,Diagonalized Hotelling’s T^2 test,Regularized Hotelling’s T^2 test,Robust test statistic,Spatial depth

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