Minimax risk over quadratically convex sets |
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Authors: | S Reshetov |
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Institution: | (3) Univ. Vienna, Vienna, Austria |
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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 N(0, 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?L( P) \sup {\Re_L}\left( \Pi \right) , where ?L( P) {\Re_L}\left( \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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Keywords: | |
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