Adaptive estimation of linear functionals under different performance measures
نویسندگان
چکیده
zi being independent and identically distributed standard normal random variables and M a finite or countably infinite index set. In particular, for these models minimax theory for mean squared error, confidence intervals and probabilistic error can all be precisely characterized by a modulus of continuity introduced by Donoho and Liu (1991). More specifically, for any linear functional T and convex parameter space F the minimax mean squared error is of order ø(1= ffiffiffi n p , F ) where the modulus ø(E, F ) is defined by ø(E, F ) 1⁄4 sup fjTg Tf j : kg f k2 < E; f , g 2 Fg, (3)
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