文章基本信息

标题：Localising change points in piecewise polynomials of general degrees
本地全文：下载
作者：Yi Yu ; Sabyasachi Chatterjee ; Haotian Xu 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：1855-1890
DOI：10.1214/21-EJS1963
语种：English
出版社：Institute of Mathematical Statistics
摘要：In this paper we are concerned with a sequence of univariate random variables with piecewise polynomial means and independent sub-Gaussian noise. The underlying polynomials are allowed to be of arbitrary but fixed degrees. All the other model parameters are allowed to vary depending on the sample size. We propose a two-step estimation procedure based on the ℓ0-penalisation and provide upper bounds on the localisation error. We complement these results by deriving global information-theoretic lower bounds, which show that our two-step estimators are nearly minimax rate-optimal. We also show that our estimator enjoys near optimally adaptive performance by attaining individual localisation errors depending on the level of smoothness at individual change points of the underlying signal. In addition, under a special smoothness constraint, we provide a minimax lower bound on the localisation errors. This lower bound is independent of the polynomial orders and is sharper than the global minimax lower bound.
关键词：change point;minimax;piecewise polynomial