On the minimax regret estimation of a restricted normal mean, and implications
AbstractConsider estimating the mean of a normal distribution with known variance, when that mean is known to lie in a bounded interval. In a decision-theoretic framework we study finite sample properties of a class of nonlinear' estimators. These estimators are based on thresholding techniques which have become very popular in the context of wavelet estimation. Under squared errorloss we show that there exists unique minimax regret solution for the problem of selecting the threshold. For comparison, the behaviour' of linear shrinkers is also investigated. In special cases we illustrate the implications of our results for the problem of estimating the regression function in a nonparametric situation. This is possible since, as usual, a, coordinatewise application of the scalar results leads immediately to results for multivariate (sequence space) problems. Then it is well known that orthogonal transformations can be employed to turn statements about estimation over coefficient bodies in sequence space into statements about estimation over classes of smooth functions in noisy data. The performance of the proposed minimax regret optimal curve estimator is demonstrated by simulated data examples. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,81.
Date of creation: 2002
Date of revision:
Bounded normal mean; soft thresholding; minimax regret decision theory; non linear estirnation; nonparametric regression; orthogonal series estimation;
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- Droge, Bernd, 2006. "Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 83-92, January.
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