The Annals of Statistics

Change-point estimation under adaptive sampling

Yan Lan, Moulinath Banerjee, and George Michailidis

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 37, Number 4 (2009), 1752-1791.

Dates
First available in Project Euclid: 18 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1245332832

Digital Object Identifier
doi:10.1214/08-AOS602

Mathematical Reviews number (MathSciNet)
MR2533471

Zentralblatt MATH identifier
1168.62018

Subjects
Primary: 62F12: Asymptotic properties of estimators 62K99: None of the above, but in this section

Keywords
Adaptive sampling change point estimation multistage procedure Skorokhod topology two-stage procedure zoom-in

Citation

Lan, Yan; Banerjee, Moulinath; Michailidis, George. Change-point estimation under adaptive sampling. Ann. Statist. 37 (2009), no. 4, 1752--1791. doi:10.1214/08-AOS602. https://projecteuclid.org/euclid.aos/1245332832


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