Abstract
The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions with relative LINEX loss and fixed cost for each observation is considered in this article. Optimal, nearly optimal, and asymptotically pointwise optimal procedures with deterministic stopping rules are derived, and the approximate optimal procedures are shown to be asymptotically nondeficient in the sense of Woodroofe (1981). In addition, a robust procedure with a deterministic stopping rule, which does not depend on the parameters of the prior distribution, is proposed, and the asymptotic second-order expansion of the corresponding Bayes risk is obtained.
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