报告题目：Nonparametric Tests for Equality of Conditional Distributions

报告时间：2024-11-25   14:00-15:30

报 告 人：宋晓军  副教授（北京大学）

报告地点：数学院二楼报告厅

Abstract: We propose nonparametric tests for the equality of two conditional distributions. To avoid the estimation of conditional density functions, we transform the null hypothesis into an equivalent characterization that a function involving only unconditional expectations equals zero everywhere. Based on an empirical analog of this function, which is √N−consistent and converges weakly to a Gaussian limit, we construct the Kolmogorov-Smirnov (KS) and Cram'{e}r-von Mises (CvM) statistics. The critical values are computed by a multiplier bootstrap procedure. The proposed KS and CvM tests are proved to be asymptotically size-controlled and consistent against any fixed alternative, and we also study the local power. Monte Carlo experiments illustrate good performances of these tests in finite samples.