A0293
Title: A distance and kernel-based framework for global and local two-sample conditional distribution testing
Authors: Xianyang Zhang - Texas A\&M University (United States) [presenting]
Jian Yan - Cornell University (United States)
Zhuoxi Li - Xiamen University (China)
Abstract: Testing for the equality of two conditional distributions is critical in numerous modern applications such as transfer learning and program evaluation. However, this fundamental problem has surprisingly received little attention in the literature. The primary objective is to establish a distance and kernel-based framework for two-sample conditional distribution testing that is adaptable to multivariate distributions and allows for heterogeneity in the marginal distributions. Two metrics are proposed, the conditional generalized energy distance and the conditional maximum mean discrepancy, which completely characterize the homogeneity of two conditional distributions. Utilizing these metrics, local and global tests are developed that can identify local and global discrepancies between two conditional distributions. In theory, the convergence rates, as well as the asymptotic distributions of the local and global tests, are derived under both the null and alternative hypotheses. To approximate the finite-sample distributions of the test statistics, a novel local bootstrap procedure is employed. The proposed local and global two-sample conditional distribution tests demonstrate reliable performance through simulations and real data analysis.
