Change-point problem and boostrap

Abstract

We consider a class of simple estimators of the change-point m in a sequence of n independent random variables X1,Xn satisfying E(Xi) = 0 for i = 1,,m and E(Xi) = 0+n for i = m +1,n. (0 and n are unknown). We obtain rates of consistency for the estimator, derive its limiting distribution and show that the bootstrap approximation is asymptotically valid. The results are illustrated by some simulations.