On the Square-Integrable Measure of the Divergence of Two Nuclear Estimations of the Bernoulli Regression Functions

Abstract

We establish the limit distribution of the square-integrable deviation of two nonparametric nuclear-type estimations for the Bernoulli regression functions. A criterion is proposed for the verification of the hypothesis of equality of two Bernoulli regression functions. We study the problem of verification and, for some “close” alternatives, investigate the asymptotics of the power.