Tests of homogeneity and change-point inference

Abstract

We study sequences of independent observations and test whether the observations stem from the same underlying probability distribution. We focus on being able to detect a potential sudden change in the parameters of the distribution, which we call a change-point. Before constructing a test, we define a focus parameter which captures the aspect of the distribution that we want to test. We construct a monitoring process for our focus parameter that converges to a Brownian bridge under the hypothesis of omogeneity. We then use our monitoring process to construct a test statistic for testing homogeneity. We look at the power of our hypothesis test, compared to other tests. We look at how our monitoring process behaves when the null hypothesis is false and suggest a way to estimate the change-point based on the process. We describe two different ways to assess the uncertainty around an estimated change-point with confidence curves.