A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum

We consider the problem of testing equality conditional distributions a response variable given vector covariates between two populations. Such hypothesis can be motivated from various machine learning and statistical inference scenarios, including transfer causal predictive inference. develop nonparametric test procedure inspired conformal prediction framework. The construction our statistic combines recent developments in with novel choice conformity score, resulting weighted rank-sum that is valid powerful under general settings. To knowledge, this first successful attempt using for hypotheses beyond exchangeability. Our method suitable modern scenarios where data has high dimensionality large sample sizes, effectively combined existing classification algorithms to find good score functions. performance proposed demonstrated numerical examples. Supplementary materials article are available online.