  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 presented and combined with
consistent point estimators of the conditional kernel mean map, in order 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
for any sample size. We also prove that both proposed techniques are consistent
under weak statistical assumptions, i.e., the type II error probabilities
pointwise converge to zero.
