SMU SOE Seminar Series (February 11, 2026): Nonparametric Tests for Equality of Conditional Distributions

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ABSTRACT

This paper proposes consistent nonparametric tests for the equivalence of conditional distributions that are easy to implement and computationally friendly in practice. To avoid the difficulty caused by estimating conditional density functions, we transform the null hypothesis into an equivalent characterization. We construct the Kolmogorov–Smirnov (KS) and the Cramer–von Mises (CvM) test statistics and establish their asymptotic distributions based on the two-sample U-process theory. The critical values are constructed through a multiplier bootstrap method. The proposed KS and CvM tests are proved to be asymptotically size controlled and consistent. Monte Carlo experiments illustrate the good performance of the tests in finite samples. In an empirical application, we apply our method to test the covariate balancing condition in propensity score matching.