A Sequential Probability Ratio Test for Sparse Gaussian Mixtures

Wenhua Jiang, Cun-Hui Zhang
2022 Statistica sinica  
We develop a one-sided sequential probability ratio test (SPRT) for detecting the presence of rare and weak signals. We prove that the test is consistent throughout the detectable region of the sparse Gaussian mixtures. This makes an interesting connection between the test of power one and the higher criticism. Unlike existing methods which uses simulated critical values, for the SPRT, the actual size of type I error is always strictly less than the nominal level. We approximate the ratio
more » ... ate the ratio between the actual size and the nominal level by nonlinear renewal theory. The accuracy of the approximation is shown by simulation. The strong power of the SPRT for moderately sparse signals is demonstrated and explained.
doi:10.5705/ss.202019.0218 fatcat:ksspsqrrnbcwxbvnnkxgkepaum