About Testing the Hypothesis of Equality of Two Bernoulli Regression Curves

Abstract

The limiting distribution of an integral square deviation between two kernel type estimators of Bernoulli regression functions is established in the case of two independent samples. The criterion of testing is constructed for both simple and composite hypotheses of equality of two Bernoulli regression functions. The question of consistency is studied. The asymptotics of behavior of the power of test is investigated for some close alternatives.

Keywords: Bernoulli Regression Function, Power of Test, Consistency, Composite Hypothesis