Statistics Colloquium

Abstract:  While change points occur in many scientific studies, statistical inference of a change point based on staggered entry data with type I censoring has been relatively modest, partly due to its diverse modality and a lack of proper technical tools. We present an asymptotic test based on a profile log-likelihood ratio process that converges weakly to a non-stationary Gaussian process. The limiting process can be mapped to an Orstein-Uhlenbeck (O-U) process with a simple transformation, and the critical values can be obtained from the supremum of the O-U process. We use two well-known medical data sets to illustrate the methods, and discuss the advantages of using a probability model that has a change point.