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Statistical estimators with asymptotically minimum \(d\)-risk. (English. Russian original) Zbl 0805.62030

Theory Probab. Appl. 38, No. 1, 118-128 (1993); translation from Teor. Veroyatn. Primen. 38, No. 1, 20-32 (1993).
The authors consider the problem of estimating a real parameter using the \(d\)-posterior risk (or \(d\)-risk for short) which is defined by the conditional mean of the loss function with respect to the decision function of the statistical procedure, that is, the mean value of the loss for statistical experiments. The definitions of estimators with uniformly minimum and asymptotically minimum \(d\)-risks are improved so that they are independent of the choice of fixed versions of conditional means in the representations of \(d\)-risks of estimators. A construction of the estimator with asymptotically minimum \(d\)-risk in the class of regular estimators is also given.

MSC:

62F12 Asymptotic properties of parametric estimators
62C10 Bayesian problems; characterization of Bayes procedures
62F10 Point estimation
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