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Minimax estimation of the mean of a general distribution when the parameter space is restricted. (English) Zbl 0621.62030
Consider the one-dimensional additive model $$Y=\theta +X$$ where $$| \theta | \leq s$$ and X has a specified distribution with $$EX=0$$, $$EX^ 2=1$$ and $$EX^ 4<\infty$$. The authors study minimax estimation of mean $$\theta$$. They extend results obtained by P. J. Bickel, Ann. Stat. 9, 1301-1309 (1981; Zbl 0484.62013) for minimax estimation of the mean of a normal distribution when the parameter space is restricted. They obtain a class of estimators which are asymptotically minimax for $$\theta$$ and show that the results obtained by Bickel remain valid without the normality assumption.
Reviewer: B.L.S.Prakasa Rao

MSC:
 62F10 Point estimation
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