Asymptotic Behavior of the Summarized Square Error in Dependence Dose-Effect for Indirect Observations

Abstract

The goal of this paper is to declare results of the asymptotic behavior of the summarized square error of the kernel distribution function estimator Fn(x) defined by SUm = m j =1(Fn(xj).F(xj))2, where F(x) is the unknown distribution function of a random variable X, ѓЦ(x) is the weight function in dose-response dependence on the sample U(n) = {(Wi, Yi), 1 . i . n}, Wi = I(Xi < Ui) is the indicator of even (Xi < Ui) and Y is a random variable, statistically dependant by U. We apply this result to test goodness-of-fit of the distribution function F(x).