FixedWidth Confidence Interval of P(X < Y) under a Data Dependent Adaptive Allocation Design

Abstract

The present article is related to a nonparametric fixed-width confidence interval estimation of the parameter µ = P(X < Y ) = R F(y)dG(y), where F and G are two unknown continuous distribution functions. The estimation procedure is based on a sample obtained under some non-iid adaptive situation. We provide various asymptotic results related to the proposed procedure and compare it with a non-adaptive procedure.