Minimax recovery of blurred signal from discrete noisy data

E. Belitser

doi:10.1080/10485250108832870

Minimax recovery of blurred signal from discrete noisy data

E. Belitser

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

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Abstract

The problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise is considered. The unknown function is assumed to belong to a hyperrectangle in L 2-([0,l]). Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose an estimator and show that its maximal risk attains asymptotically the minimax risk. The results are illustrated by examples. Keywords: Blurred signal; Exact asymptotics of the minimax risk; Hyperrectangle.

Original language	English
Pages (from-to)	647-666
Number of pages	20
Journal	Journal of Nonparametric Statistics
Volume	13
Issue number	5
DOIs	https://doi.org/10.1080/10485250108832870
Publication status	Published - 2001

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10.1080/10485250108832870

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title = "Minimax recovery of blurred signal from discrete noisy data",

abstract = "The problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise is considered. The unknown function is assumed to belong to a hyperrectangle in L 2-([0,l]). Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose an estimator and show that its maximal risk attains asymptotically the minimax risk. The results are illustrated by examples. Keywords: Blurred signal; Exact asymptotics of the minimax risk; Hyperrectangle.",

author = "E. Belitser",

year = "2001",

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AB - The problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise is considered. The unknown function is assumed to belong to a hyperrectangle in L 2-([0,l]). Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose an estimator and show that its maximal risk attains asymptotically the minimax risk. The results are illustrated by examples. Keywords: Blurred signal; Exact asymptotics of the minimax risk; Hyperrectangle.

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DO - 10.1080/10485250108832870

M3 - Article

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VL - 13

SP - 647

EP - 666

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

IS - 5

ER -

Minimax recovery of blurred signal from discrete noisy data

Abstract

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