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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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DOI

10.1002/hed.22924

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1573-8795

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Minimax risk over quadratically convex sets

Authors: S Reshetov
Publish Date: 2010/05/25
Volume: 167, Issue: 4, Pages: 537-542
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Abstract

We consider the problem of estimating a vector θ = θ1 θ2… ∈ Θ ⊂ l 2 from observations y i = θ i + σ i x i i = 1 2… where the random values x i are N0 1 independent and identically distributed the parametric set Θ is compact orthosymmetric convex and quadratically convex We show that in that case the minimax risk is not very different from sup Re Lleft Pi right where Re Lleft Pi right is the minimax linear risk in the same problem with parametric set Π and sup is taken over all the hyperrectangles Π ⊂ Θ Donoho Liu and McGibbon 1990 have obtained this result for the case of equal σ i i = 1 2… Bibliography 4 titles

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  11. Probabilistic approach to viscosity solutions of the Cauchy problems for systems if fully nonlinear parabolic equations
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  19. On some constructive methods for the matrix Riemann–Hilbert boundary-value problem
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