Jump or Kink: Super-Efficiency in Segmented Linear Regression Break-Point Estimation

• Activity Number: 140 - Change-Points in Multivariate and High-Dimensional Data
• Type: Invited
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yining Chen*
• Companies: London School of Economics
• Keywords: segmented regression; change-point; super-efficiency; minimax rates; structure change

Abstract

We consider the problem of segmented linear regression with the focus on estimating of the location of the break-point(s). Let n be 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 values, depending on whether the structural change is a jump or a kink. We discuss the implications and the potential remedy. We then illustrate this phenomenon in the multivariate and high-dimensional settings, and extend our results to segmented polynomial regression models.