在幂绝对误差损失(PAEL)下的指数分布中均值的最小风险点估计(MRPE)，这是由于估计加上采样成本造成的

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2020-04-02 DOI:10.1080/07474946.2020.1766930

N. Mukhopadhyay, Ya. G. Khariton

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引用次数: 8

摘要

摘要我们首先回顾了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）方法的渐近性质。这类功率绝对误差损失（PAEL）包括平方误差损失（SEL）和绝对误差损耗（AEL）加上采样成本。我们证明了与纯序列MRPE问题相关的渐近二阶效率性质和渐近一阶风险效率性质。为了操作方便，我们随后实现了一种加速序列MRPE方法，并证明了类似的渐近二阶效率性质和渐近一阶风险效率性质。我们通过模拟进行了广泛的数据分析，并使用癌症数据进行了说明。

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Minimum risk point estimation (MRPE) of the mean in an exponential distribution under powered absolute error loss (PAEL) due to estimation plus cost of sampling

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.

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.