Detecting a change in regression: First-order optimality
成果类型：
Article
署名作者：
Yakir, B; Krieger, AM; Pollak, M
署名单位：
Hebrew University of Jerusalem; University of Pennsylvania
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1999
页码：
1896-1913
关键词：
摘要：
Observations are generated according to a regression with normal err or as a Function of time, when the process is in control. The process potentially changes at some unknown point of time and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions. The problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm. A bound on the expected delay is first obtained. It iv then shown that the cusum and Shiryayev-Roberts procedures achieve this bound to first order.