An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Srawan Kumar Bishnoi, N. Mukhopadhyay
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引用次数: 0

Abstract

Abstract We develop a new class of purely sequential methodologies under an assumption that the population distribution belongs to a location-scale family. Both asymptotic first-order and second-order theories are put forward with substantial generality under a big and unified tent that successfully lead to a broad set of illustrations. After we identify an appropriately defined optimal strategy under this unified structure, we introduce applications that handle a variety of interesting inference problems. These are associated with, but not limited to, the following areas: (a) the fixed-width confidence interval (FWCI) estimation, (b) the minimum risk point estimation (MRPE), (c) the fixed-size confidence region (FSCR) estimation, (d) multiple comparisons, and (e) selecting the best normal treatment (StBNT). In illustrations (a)–(d), we have highlighted a number of choices of population distributions. Some illustrations are accompanied with data analyses.
具有渐近二阶性质的最优纯序列策略:在统计推断和数据分析中的应用
摘要在假设人口分布属于一个位置尺度的家族的情况下,我们提出了一类新的纯序列方法。渐近一阶和二阶理论都是在一个大而统一的框架下提出的,具有相当的普遍性,并成功地给出了一组广泛的例证。在我们确定了这个统一结构下适当定义的最优策略之后,我们将介绍处理各种有趣推理问题的应用程序。这些与但不限于以下领域相关:(a)固定宽度置信区间(FWCI)估计,(b)最小风险点估计(MRPE),(c)固定大小置信区间(FSCR)估计,以及(d)多重比较,以及(e)选择最佳正态治疗(StBNT)。在插图(a)-(d)中,我们强调了人口分布的一些选择。一些插图附有数据分析。
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
20
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.
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