Abstract We have designed a sequential minimum risk point estimation (MRPE) strategy for the unknown mean of a normal population having its variance unknown too. This is developed under a Linex loss plus linear cost of sampling. A number of important asymptotic first-order and asymptotic second-order properties' characteristics have been developed and proved thoroughly. Extensive sets of simulations tend to validate nearly all of these asymptotic properties for small to medium to large optimal fixed sample sizes.

中文翻译：

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Linex 损失加采样成本下正态均值的顺序最小风险点估计 (MRPE) 方法：一阶和二阶渐近

摘要 我们为方差未知的正态总体的未知均值设计了一种序贯最小风险点估计（MRPE）策略。这是在 Linex 损失加上采样的线性成本下开发的。一些重要的渐近一阶和渐近二阶性质的特性已经得到充分的发展和证明。大量模拟倾向于验证几乎所有这些渐近特性，适用于小到中到大的最佳固定样本量。