Bayes double sample estimation procedures (Q796227)

Let \(X=(X_ 1,...,X_ d)\) be a random vector with distribution \(dP_{\theta}(x)=\exp(x\cdot \theta -M(\theta))d\mu(x)\). Given the conjugate prior distribution of \(\theta\) and a loss function depending both on an error of estimation and on the cost of sampling, the Bayesian two-stage estimate of \(EX_ 1\) is constructed. Applications to binomial and normal cases are presented.