On estimation with balanced loss functions

✍ Scribed by Dipak K Dey; Malay Ghosh; William E Strawderman

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 76 KB
• Volume: 45
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00047-4

✦ Synopsis

Zellner ((1994) in: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390), introduced the notion of a balanced loss function in the context of a general linear model to re ect both goodness of ÿt and precision of estimation. We study this notion from the perspective of unifying a variety of results both frequentist and Bayesian. We show in broad generality that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions re ecting only precision of estimation. Several examples are given for normal error structures and more generally for spherically symmetric error distribution.