In many high-dimensional applications, it is of interest to test whether the mean vectors of two populations are equal. However, the presence of unknown and unequal block diagonal covariance matrices can complicate the testing procedure, and choosing an appropriate test becomes challenging. The study aimed to investigate the performance of tests for equality of two high-dimensional mean vectors with unknown and unequal block diagonal covariance matrices. The study focused on three tests: T1 proposed by Srivastava, Katayama, and Kano (2013), T2 proposed by Hu, Bai, Wang, and Wang (2017), and T3 proposed by Ahmad (2019). The study included both cases: equal and unequal sample sizes. The effect of block size in the covariance matrix on the performance of the tests was also studied. The data was gathered using two independent high-dimensional samples based on multivariate normality and unequal covariance matrices with block diagonal structure. The number of variables studied ranged from 50 - 500 and the sample size was 20 - 200. The results showed that, for equal sample sizes, both of the tests T1 and T2 performed well, and when the sample size exceeds 20, the test T1 performed slightly higher than T2. When two sample sizes were unequal, the test T2 outperformed the tests T1 and T3. A study of the effect of block size discovered that larger block sizes resulted in poor test performance and the influence of block size diminishes as sample size increases.

High-dimensional mean vectors

Unequal covariance matrices

Block diagonal covariances

Covariance matrix block size

high-dimensional data