Change-point problem and bootstrap

Abstract

We consider a class of simple estimators of the change-point m in a sequence of n independent random variables X1…,X n satisfying E(X i ) = θ0 for i = 1,…,m and E(X i ) = θ0+δ n for i = m +1,…n. (θ0 and δ 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.