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April 2021 Minimax rates in sparse, high-dimensional change point detection
Haoyang Liu, Chao Gao, Richard J. Samworth
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Ann. Statist. 49(2): 1081-1112 (April 2021). DOI: 10.1214/20-AOS1994

Abstract

We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for n independent, p-variate Gaussian observations. This rate exhibits a phase transition when the sparsity level is of order ploglog(8n) and has a very delicate dependence on the sample size: in a certain sparsity regime, it involves a triple iterated logarithmic factor in n. Further, in a dense asymptotic regime, we identify the sharp leading constant, while in the corresponding sparse asymptotic regime, this constant is determined to within a factor of 2. Extensions that cover spatial and temporal dependence, primarily in the dense case, are also provided.

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Haoyang Liu. Chao Gao. Richard J. Samworth. "Minimax rates in sparse, high-dimensional change point detection." Ann. Statist. 49 (2) 1081 - 1112, April 2021. https://doi.org/10.1214/20-AOS1994

Information

Received: 1 July 2019; Revised: 1 June 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1994

Subjects:
Primary: 62C20

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 2 • April 2021
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