On estimation with weighted balanced-type loss function

Mohammad Jafari Jozani, Éric Marchand and Ahmad Parsian

Statistics & Probability Letters, 2006, vol. 76, issue 8, 773-780

Abstract: For estimating an unknown parameter [theta], we introduce and motivate the use of the balanced-type loss function: , where 0[less-than-or-equals, slant][omega][less-than-or-equals, slant]1, q([theta]) is a positive weight function, and [delta]0 is a general "target" estimator. Developments and various examples are given with regards to the issues of admissibility, dominance, Bayesianity, and minimaxity. In many cases, as in Dey et al. [1999. On estimation with balanced loss functions. Statist. Probab. Lett. 45, 97-101], we show that results for loss L[omega],[delta]0 may be inferred directly from corresponding results for weighted squared error loss (i.e., [omega]=0). Specific issues related to constrained parameter spaces, which include the choice of the target estimator, are addressed. Finally, we derive minimax estimators of a bounded normal mean [theta] under loss L[omega],[delta]0 with [delta]0 being the maximum-likelihood estimator of [theta].

Keywords: Balanced; loss; function; Admissibility; Bayes; estimator; Minimax; estimation; Constrained; parameter; space (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (13)

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