On The Bayes Risk Of Fixed Sample Size And Sequential Procedures In Pointwise Estimation

International audienceThe estimation of the mean 6 of a one parameter exponential family of distributions is considered. The loss function used is of the form l(a,B) = K(a-0) where K is some smooth, symmetric function. We give second order expansions of the Bayes risk in the fixed sample size case. For the Sequential case, we give an upper bound for the Bayes risk of the optimal procedure; the cost per observation is assumed to be equal to c,c> 0