Non-asymptotic sub-Gaussian error bounds for hypothesis testing

Yanpeng Li; Boping Tian

doi:10.1016/j.spl.2022.109586

Non-asymptotic sub-Gaussian error bounds for hypothesis testing

Yanpeng Li^*
, Boping Tian

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Using the sub-Gaussian norm of the Bernoulli random variable, this paper presents the explicit and informative error lower bounds for binary and multiple hypothesis testing in terms of the KL divergence non-asymptotically. Some numerical comparisons are also demonstrated.

Original language	English
Article number	109586
Journal	Statistics and Probability Letters
Volume	189
DOIs	https://doi.org/10.1016/j.spl.2022.109586
State	Published - Oct 2022
Externally published	Yes

Keywords

Fano's inequality
KL divergence
Pinsker's bound
Sub-Gaussian

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10.1016/j.spl.2022.109586

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title = "Non-asymptotic sub-Gaussian error bounds for hypothesis testing",

abstract = "Using the sub-Gaussian norm of the Bernoulli random variable, this paper presents the explicit and informative error lower bounds for binary and multiple hypothesis testing in terms of the KL divergence non-asymptotically. Some numerical comparisons are also demonstrated.",

keywords = "Fano's inequality, KL divergence, Pinsker's bound, Sub-Gaussian",

author = "Yanpeng Li and Boping Tian",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = oct,

doi = "10.1016/j.spl.2022.109586",

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AU - Tian, Boping

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AB - Using the sub-Gaussian norm of the Bernoulli random variable, this paper presents the explicit and informative error lower bounds for binary and multiple hypothesis testing in terms of the KL divergence non-asymptotically. Some numerical comparisons are also demonstrated.

KW - Fano's inequality

KW - KL divergence

KW - Pinsker's bound

KW - Sub-Gaussian

UR - https://www.scopus.com/pages/publications/85132932126

U2 - 10.1016/j.spl.2022.109586

DO - 10.1016/j.spl.2022.109586

M3 - 文章

AN - SCOPUS:85132932126

SN - 0167-7152

VL - 189

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109586

ER -

Non-asymptotic sub-Gaussian error bounds for hypothesis testing

Abstract

Keywords

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