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2015 A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection
Clément Marteau, Theofanis Sapatinas
Statist. Surv. 9: 253-297 (2015). DOI: 10.1214/15-SS112

Abstract

We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach) and the minimax separation rate (asymptotic approach) that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa.

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Clément Marteau. Theofanis Sapatinas. "A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection." Statist. Surv. 9 253 - 297, 2015. https://doi.org/10.1214/15-SS112

Information

Received: 1 January 2015; Published: 2015
First available in Project Euclid: 19 January 2016

zbMATH: 1329.62169
MathSciNet: MR3452237
Digital Object Identifier: 10.1214/15-SS112

Subjects:
Primary: 62G05, 62K20

Rights: Copyright © 2015 The author, under a Creative Commons Attribution License

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