• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.427-440
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• 2024

The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t - M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.191-200
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• 1993

An asymptotic estimation problem of the unknown mean is studied under a general loss function. The proof of this result is based on the asymptotic expansion of the risk function. Also conditions for second order admissibility and minimaxity of a class of estimators depending only on the sample mean are established.