A robust Pearson correlation test for a general point null using a surrogate bootstrap distribution

In this note we present a robust bootstrap test with good Type I error control for testing the general hypothesis H₀: ρ = ρ0. In order to carry out this test we use what is termed a surrogate bootstrap distribution. The test was inspired by the studentized permutation for testing H₀: ρ = 0, which was proven to be exact in certain scenarios and asymptotically correct overall. We show that the bootstrap based test is robust to a variety of distributional scenarios in terms of proper Type I error control.