2021/04/30 by Xiaoli Gao, Ejaz Ahmed, Gao, Xiaoli +1
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2104.14827
openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the recovery of a joint piece-wise linear trend from a time series using L1 regularization approach, called L1 trend filtering (Kim, Koh and Boyd, 2009). We provide some sufficient conditions under which a L1 trend filter can be well-behaved in terms of mean estimation and change point detection. The result is two-fold: for the mean estimation, an almost optimal consistent rate is obtained; for the change point detection, the slope change in direction can be recovered in a high probability. In addition, we show that the weak irrepresentable condition, a necessary condition for LASSO model to be sign consistent (Zhao and Yu, 2006), is not necessary for the consistent change point detection. The performance of the L1 trend filter is evaluated by some finite sample simulations studies.