Bayes sequential estimation for a particular exponential family of distributions under LINEX loss

The problem of sequentially estimating an unknown distribution parameter of a particular exponential family of distributions is considered under LINEX loss function for estimation error and a cost c > 0 for each of an i.i.d. sequence of potential observations X ₁, X ₂, . . . A Bayesian approach is adopted and conjugate prior distributions are assumed. Asymptotically pointwise optimal and asymptotically optimal procedures are derived.