Purely Sequential and Two-Stage Bounded-Length Confidence Intervals for the Bernoulli Parameter with Illustrations from Health Studies and Ecology
Purely Sequential and Two-Stage Bounded-Length Confidence Intervals for the Bernoulli Parameter with Illustrations from Health Studies and Ecology
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伯努利参数的纯序贯和两阶段有界长度置信区间，以健康研究和生态学为例
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发表时间：
2015
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通讯作者：
Swarnali Banerjee
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作者：
N. Mukhopadhyay;Swarnali Banerjee
虫害影响食物和营养的供应以及环境，从而对人类、动物、植物种群和其他自然资源的健康的生态平衡产生深刻影响。例如，众所周知，估计（i）存在侵染的概率，（ii）患病的机会，和（iii）复发的机会在昆虫学和健康研究中非常重要。它们通常涉及由Bernoulli（p）分布建模的二进制数据，其中p是未知参数，（0 1），）我们为p建立了大约（100（1-α），1%）个置信区间（（L_{N}，U_{N}）），使得（0<L_{N}<U_{N}<1）和（U_{N}-L_{N}le d）w.p.1。这里，N是通过两阶段和纯序贯采样策略获得的适当设计和确定的停止变量。所提出的两阶段和纯序列的有界长度置信区间方法被证明是享受渐近一阶效率和渐近一致性属性。然后，我们通过分析模拟产生的数据，提出了新方法的摘要性能。我们还实现了三个真实的数据集的大小小到中等到大的建议的方法。
Infestation affects supplies of food and nutrition as well as the environment, thus making a deep impact in the ecological balance of the health of humans, animals, plant populations, and other natural resources. It is well known, for example, that estimation of (i) the probability of presence of infestation, (ii) the chance of getting a disease, and (iii) the chance of a relapse are very important in entomology and health studies. They frequently involve binary data modelled by a Bernoulli(p) distribution where p is an unknown parameter, (0 1),) we develop approximately (100(1-alpha ),\%) confidence intervals ((L_{N},U_{N})) for p such that (0<L_{N}<U_{N}<1) and (U_{N}-L_{N}le d) w.p.1. Here, N is a properly designed and determined stopping variable obtained via both two-stage and purely sequential sampling strategies. The proposed two-stage and purely sequential bounded-length confidence interval methodologies are shown to enjoy both asymptotic first-order efficiency and asymptotic consistency properties. Then, we present summary performances of the new methodologies by analyzing data generated from simulations. We have also implemented the proposed methodologies for three real data sets of size small to moderate to large.