Olusola Samuel MAKİNDE, Odunayo Sile OMOTOSO

On some Diagonalized and Regularized Hotelling’s ?? Tests of Location for High Dimensional Data

A widely used statistical test of hypothesis for location parameter in ℝ?is the Hotelling’s ?2test. 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 implementwhendimensionisgreaterthansamplesize.Asaremedialmeasure, diagonalized and regularized Hotelling’s ?2tests were proposed. In this paper, powers of regularized and diagonalized Hotelling’s ?2tests are compared with the usual Hotelling’s ?2testin low dimension and the usual Hotelling’s ?2perform much better. It is observed that diagonalized Hotelling’s ?2test may have low power for mixture distributions. Due to a comparative performance of regularized and diagonalized Hotelling’s ?2tests, robust versions of diagonalized and regularized Hotelling’s ?2tests are proposed in high dimension in the presence of outliers. The powers of these tests were compared using simulated as well as real datasets.

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