  The paper studies binary classification and aims at estimating the underlying
regression function which is the conditional expectation of the class labels
given the inputs. The regression function is the key component of the Bayes
optimal classifier, moreover, besides providing optimal predictions, it can
also assess the risk of misclassification. We aim at building non-asymptotic
confidence regions for the regression function and suggest three kernel-based
semi-parametric resampling methods. We prove that all of them guarantee regions
with exact coverage probabilities and they are strongly consistent.
