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Obtaining minimax lower bounds: a review

Authors
Kim, Arlene K. H.
Issue Date
9월-2020
Publisher
SPRINGER HEIDELBERG
Keywords
Minimax lower bounds; Le Cam; Assouad; Fano; Two directional method; private estimation
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.49, no.3, pp.673 - 701
Indexed
SCIE
SCOPUS
KCI
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
49
Number
3
Start Page
673
End Page
701
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/53699
DOI
10.1007/s42952-019-00027-7
ISSN
1226-3192
Abstract
Minimax lower bounds determine the complexity of given statistical problems by providing fundamental limit of any procedures. This paper gives a review on various aspects of obtaining minimax lower bounds focusing on a recent development. We first introduce classical methods, then more involved lower bound constructions such as testing two mixtures, two directional method, and global metric entropy method are provided with various examples including manifold learning, approximation sets and neural nets. In addition, we consider two different types of restrictions on the set of estimators. In particular, we consider the lower bounds when the set of estimators is required to be linear, and a private version of minimax lower bounds is discussed.
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