Minimax estimation of the mean of a general distribution when the parameter space is restricted. (English) Zbl 0621.62030

Melkman, Avraham A.; Ritov, Ya’acov

Ann. Stat. 15, 432-442 (1987).

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

Keywords:

restricted parameter space; mean estimation; one-dimensional additive model; minimax estimation; asymptotically minimax