  In this paper we suggest two statistical hypothesis tests for the regression
function of binary classification based on conditional kernel mean embeddings.
The regression function is a fundamental object in classification as it
determines both the Bayes optimal classifier and the misclassification
probabilities. A resampling based framework is applied and combined with
consistent point estimators for the conditional kernel mean map to construct
distribution-free hypothesis tests. These tests are introduced in a flexible
manner allowing us to control the exact probability of type I error. We also
prove that both proposed techniques are consistent under weak statistical
assumptions, i.e., the type II error probabilities pointwise converge to zero.
