Lower bounds on Bayes risks for estimating a normal variance: With applications Academic Article uri icon


  • [Brown and Gajek (1990) gave useful lower bounds on Bayes risks, which improve on earlier bounds by various authors. Many of these use the information inequality. For estimating a normal variance using the invariant quadratic loss and any arbitrary prior on the reciprocal of the variance that is a mixture of Gamma distributions, we obtain lower bounds on Bayes risks that are different from Borovkov-Sakhanienko bounds. The main tool is convexity of appropriate functionals as opposed to the information inequality. The bounds are then applied to many specific examples, including the multi-Bayesian setup (Zidek and his coauthors). Subsequent use of moment theory and geometry gives a number of new results on efficiency of estimates which are linear in the sufficient statistic. These results complement earlier results of Donoho, Liu and MacGibbon (1990), Johnstone and MacGibbon (1992) and Vidakovic and DasGupta (1994) for the location case. /// Brown et Gajek (1990) ont donn des limites infrieures utiles aux risques de Bayes, qui amliorent les limites donnes prcdemment par diffrents auteurs. Plusieurs d'entre eux utilisent l'ingalit d'information. En estimant une variance normale l'aide d'une fonction de perte quadratique invariante et d'un a priori arbitraire sur l'inverse de la variance, qui est un mlange de distributions Gamma, on obtient des limites infrieures sur les risques de Bayes qui sont diffrentes des limites de Borovkov-Sakhanienko. L'outil principal est la convexit de fonctionnels appropris, et non l'ingalit de l'information. Les limites sont alors appliques diffrents exemples, dont la situation multi-Bayesienne (Zidek et co-auteurs). L'utilisation subsquente de la thorie des moments et de la gomtrie donne un certain nombre de nouveaux rsultats sur l'efficacit des estimations, qui sont linaires dans la statistique exhaustive. Ces rsultats compltent les rsultats obtenus prcdemment par Donoho, Liu et MacGibbon (1990), Johnson et MacGibbon (1992) et Vidakovic et DasGupta (1994) pour le cas de la position.]

published proceedings

  • Canadian Journal of Statistics

author list (cited authors)

  • Vidakovic, B., & Dasgupta, A.

citation count

  • 2

complete list of authors

  • Vidakovic, Brani||Dasgupta, Anirban

publication date

  • September 1995