Group for Research in Decision Analysis

Chung-Smirnov property for Bernstein Estimators of Distribution Functions

Alexandre Leblanc

In this talk, we will discuss the fact that the Chung-Smirnov property holds for Bernstein estimators of distribution functions under different conditions on the underlying distribution to be estimated. We will also discuss general results that characterize the closeness between these Bernstein estimators and the empirical distribution function in terms of the modulus of oscillation of the uniform empirical process.