A stationary bootstrap test about two mean vectors comparison with somewhat dense differences and fewer sample size than dimension

Two sample mean vectors comparison hypothesis testing problems often emerge in modern biostatistics. Many tests are proposed for detecting relatively dense signals with somewhat dense nonzero components in mean vectors differences. One kind of these tests is based on some quadratic forms about two sample mean vectors differences. Another kind of these tests is based on some quadratic forms about studentized version of two sample mean vectors differences. In this article, we propose a bootstrap test by adopting stationary bootstrap scheme to calculate p value of a typical test which is based on a quadratic form about studentized version of two sample mean vectors differences. Extensive simulations are conducted to compare performances of the bootstrap test with other existing typical tests. We also apply the bootstrap test to a real genetic data analysis about breast cancer.