|
Activity Number:
|
29
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Sunday, July 29, 2007 : 2:00 PM to 3:50 PM
|
|
Sponsor:
|
Section on Physical and Engineering Sciences
|
| Abstract - #308931 |
|
Title:
|
A Sequential Methodology for Change Point Estimation
|
|
Author(s):
|
Yan Lan*+ and Moulinath Banerjee and George Michailidis
|
|
Companies:
|
University of Michigan and University of Michigan and The University of Michigan
|
|
Address:
|
439 West Hall, Ann Arbor, MI, 48109,
|
|
Keywords:
|
adaptive sampling ; change point estimation ; two-stage procedure ; Skorohod Topology
|
|
Abstract:
|
Consider a constant regression model for a bounded covariate that has a single discontinuity. Budget constraints dictate that a total of N covariate values and corresponding responses can be obtained. The goal is to estimate accurately the location of the change-point. We propose a two-stage procedure and its properties are examined, where at the first stage a proportion of the N points are sampled and the location of the change-point estimated. Subsequently, the remaining proportion of points are sampled from an appropriately chosen neighborhood of the initial estimate and a new estimate is obtained. The asymptotic statistic of the least squares estimate is derived. The rate of convergence is improved to o(1/n^{1+\gamma}) (\gamma\in(0, 1)).The improved efficiency of the procedure is demonstrated using real and synthetic data. The methodology could be generalized to a multi-stage procedure.
|
