Nonanticipating estimation applied to sequential analysis and changepoint detection

• 成果类型: Article
• 署名作者: Lorden, G; Pollak, M
• 署名单位: California Institute of Technology; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000183
• 发表日期: 2005
• 页码: 1422-1454
• 关键词: expected sample size; renewal theory; change-point; approximations; tests

摘要

Suppose a process yields independent observations whose distributions belong to a family parameterized by theta E Theta. When the process is in control, the observations are i.i.d. with a known parameter value theta(0). When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37-41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixture-type rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.