CHANGE-POINT IN STOCHASTIC DESIGN REGRESSION AND THE BOOTSTRAP

• 成果类型: Article
• 署名作者: Seijo, Emilio; Sen, Bodhisattva
• 署名单位: Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS874
• 发表日期: 2011
• 页码: 1580-1607
• 关键词: models; CONVERGENCE; estimators; covariate; threshold; CURVES; weak

摘要

In this paper we study the consistency of different bootstrap procedures for constructing confidence intervals (CIs) for the unique jump discontinuity (change-point) in an otherwise smooth regression function in a stochastic design setting. This problem exhibits nonstandard asymptotics, and we argue that the standard bootstrap procedures in regression fail to provide valid confidence intervals for the change-point. We propose a version of smoothed bootstrap, illustrate its remarkable finite sample performance in our simulation study and prove the consistency of the procedure. The m out of it bootstrap procedure is also considered and shown to be consistent. We also provide sufficient conditions for any bootstrap procedure to be consistent in this scenario.