Detection of slightly expressed changes in random environment

Abstract

Consider a regular parametric family of distributions F(·, θ). The classical change point problem deals with observations corresponding to θ = 0 before a point of change, and θ = µ after that. We substitute the latter constant µ by a set of random variables θ i,n called a random environment assuming that E[θ i,n ] = µ n → 0. The random environment can be independent or obtained by random permutations of a given set. We define the rates of convergence and give the conditions under which the classical parametric change point algorithms apply.