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October 2009 Nonparametric estimation by convex programming
Anatoli B. Juditsky, Arkadi S. Nemirovski
Ann. Statist. 37(5A): 2278-2300 (October 2009). DOI: 10.1214/08-AOS654


The problem we concentrate on is as follows: given (1) a convex compact set X in ℝn, an affine mapping xA(x), a parametric family {pμ(⋅)} of probability densities and (2) N i.i.d. observations of the random variable ω, distributed with the density pA(x)(⋅) for some (unknown) xX, estimate the value gTx of a given linear form at x.

For several families {pμ(⋅)} with no additional assumptions on X and A, we develop computationally efficient estimation routines which are minimax optimal, within an absolute constant factor. We then apply these routines to recovering x itself in the Euclidean norm.


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Anatoli B. Juditsky. Arkadi S. Nemirovski. "Nonparametric estimation by convex programming." Ann. Statist. 37 (5A) 2278 - 2300, October 2009.


Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62024
MathSciNet: MR2543692
Digital Object Identifier: 10.1214/08-AOS654

Primary: 62G08
Secondary: 62G07 , 62G15

Keywords: Convex optimization , Estimation of linear functional , minimax estimation , Oracle inequalities , PE tomography

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 5A • October 2009
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