Detection and Localization of Changes in Conditional Distributions

We study the change point problem that considers alterations in the conditional distribution of an inferential target on a set of covariates. This paired data scenario is in contrast to the standard setting where a sequentially observed variable is analyzed for potential changes in the marginal distribution. We propose new methodology for solving this problem, by starting from a simpler task that analyzes changes in conditional expectation, and generalizing the tools developed for that task to conditional distributions. Large sample properties of the proposed statistics are derived. In empirical studies, we illustrate the performance of the proposed method against baselines adapted from existing tools. Two real data applications are presented to demonstrate its potential.