Minimax estimation in the blurred signal model

E. Belitser

Minimax estimation in the blurred signal model

E. Belitser

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.

Original language	English
Title of host publication	Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)
Editors	B. Grigelionis, J. Kubilius, V. Paulauskas, H. Pragarauskas, R. Rudzkis, V. Statulevicius
Place of Publication	Vilnius
Publisher	TEV
Pages	57-66
ISBN (Print)	9986-546-72-9
Publication status	Published - 1999

Cite this

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title = "Minimax estimation in the blurred signal model",

abstract = "We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.",

author = "E. Belitser",

year = "1999",

language = "English",

isbn = "9986-546-72-9",

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booktitle = "Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)",

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Minimax estimation in the blurred signal model. / Belitser, E.

Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998). ed. / B. Grigelionis; J. Kubilius; V. Paulauskas; H. Pragarauskas; R. Rudzkis; V. Statulevicius. Vilnius : TEV, 1999. p. 57-66.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Minimax estimation in the blurred signal model

AU - Belitser, E.

PY - 1999

Y1 - 1999

N2 - We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.

AB - We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.

M3 - Conference contribution

SN - 9986-546-72-9

SP - 57

EP - 66

BT - Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)

A2 - Grigelionis, B.

A2 - Kubilius, J.

A2 - Paulauskas, V.

A2 - Pragarauskas, H.

A2 - Rudzkis, R.

A2 - Statulevicius, V.

PB - TEV

CY - Vilnius

ER -

Minimax estimation in the blurred signal model

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