Repository logo
 

MINIMAX RATES IN SPARSE, HIGH-DIMENSIONAL CHANGE POINT DETECTION

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Liu, Haoyang 
Gao, Chao 
Samworth, Richard J 

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.

Description

Keywords

Minimax detection boundary, iterated logarithm, time series

Journal Title

ANNALS OF STATISTICS

Conference Name

Journal ISSN

0090-5364

Volume Title

49

Publisher

Institute of Mathematical Statistics

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)