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Casella, G., Hwang, J.T.G. and Robert, C. (1994) Loss Function for Set Estimation, In: Berger, J.O. and Gupta, S.S., Eds., Statistical Decision Theory and Related Topics V, Springer-Verlag, New York, 237-252.
https://doi.org/10.1007/978-1-4612-2618-5_18

has been cited by the following article:

• TITLE: Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

  AUTHORS: Fulvio De Santis, Stefania Gubbiotti

  KEYWORDS: Bayesian Inference, Decision-Theoretic Approach, Highest Posterior Density Sets, Interval Estimation, Regret

  JOURNAL NAME: Open Journal of Statistics, Vol.13 No.2, April 12, 2023

  ABSTRACT: Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses; 2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.