On the test level accuracy of the bootstrapped matched filter detector

We use Edgeworth expansions to show the higher-order accuracy of the bootstrapped matched filter (MF) detector. Specifically, the bootstrapped MF has a probability of false alarm of order 1/n distant from the design level, where n is the sample size. This results holds for bounded signals. We also show that the order is n^-3/2 for sinusoidal signals. Simulation results compare the bootstrapped MF with the classical MF. We briefly discuss the bootstrapping approach when the noise variance is unknown, when signal parameters are unknown, and when the noise is correlated