MINIMAX RATES IN SPARSE, HIGH-DIMENSIONAL CHANGE POINT DETECTION
成果类型：
Article
署名作者：
Liu, Haoyang; Gao, Chao; Samworth, Richard J.
署名单位：
University of Chicago; University of Cambridge
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/20-AOS1994
发表日期：
2021
页码：
1081-1112
关键词：
摘要：
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 root p log log (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 root 2. Extensions that cover spatial and temporal dependence, primarily in the dense case, are also provided.