Change-point problem and bootstrap
- 1 January 1995
- journal article
- research article
- Published by Taylor & Francis in Journal of Nonparametric Statistics
- Vol. 5 (2) , 123-144
- https://doi.org/10.1080/10485259508832639
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.Keywords
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