Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation
成果类型：
Article
署名作者：
Chen, Yining
署名单位：
University of London; London School Economics & Political Science
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asaa049
发表日期：
2021
页码：
215222
关键词：
摘要：
We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If n is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is O(n(-1/3)). On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either O(n(-1)) or O(n(-1/2)) for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.