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August 2009 Change-point estimation under adaptive sampling
Yan Lan, Moulinath Banerjee, George Michailidis
Ann. Statist. 37(4): 1752-1791 (August 2009). DOI: 10.1214/08-AOS602

Abstract

We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of n such measurements can be obtained. A multistage adaptive procedure is proposed, where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neighborhood. It is shown that such procedures accelerate the rate of convergence of the least squares estimate of the change-point. Further, the asymptotic distribution of the estimate is derived using empirical processes techniques. The latter result provides guidelines on how to choose the tuning parameters of the multistage procedure in practice. The improved efficiency of the procedure is demonstrated using real and synthetic data. This problem is primarily motivated by applications in engineering systems.

Citation

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Yan Lan. Moulinath Banerjee. George Michailidis. "Change-point estimation under adaptive sampling." Ann. Statist. 37 (4) 1752 - 1791, August 2009. https://doi.org/10.1214/08-AOS602

Information

Published: August 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1168.62018
MathSciNet: MR2533471
Digital Object Identifier: 10.1214/08-AOS602

Subjects:
Primary: 62F12 , 62K99

Keywords: adaptive sampling , change point estimation , multistage procedure , Skorokhod topology , two-stage procedure , zoom-in

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 4 • August 2009
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