Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.

中文翻译：

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由于估计加上抽样成本，在幂绝对误差损失 (PAEL) 下指数分布中均值的最小风险点估计 (MRPE)

摘要 我们首先回顾了在一类广义损失函数下单参数指数分布中未知均值的纯序列最小风险点估计 (MRPE) 方法的渐近特性。此类功率绝对误差损失 (PAEL) 包括平方误差损失 (SEL) 和绝对误差损失 (AEL) 以及采样成本。我们证明了与纯序列 MRPE 问题相关的渐近二阶效率特性和渐近一阶风险效率特性。为了操作方便，我们随后开始实施加速顺序 MRPE 方法并证明类似的渐近二阶效率属性和渐近一阶风险效率属性。