On Threshold Choice in Hypothesis Testing for Dynamical Systems with Small Noise

Abstract

We considered the problem of testing a simple hypothesis against composite one-sided alternative by the continuous time observations of diffusion process with small noise. Moreover, we propose a test which is asymptotically equivalent to the Neyman-Pearson test for local alternatives. The special choice of the threshold allows us to improve the rate of convergence of the first type error to the given value. The calculation of this threshold is based on the stochastic expansion of the test statistics and on the Edgeworth expansion of its distribution function.