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首页> 外文期刊>Sequential analysis >Purely Sequential and Two-Stage Fixed-Accuracy Confidence Interval Estimation Methods for Count Data from Negative Binomial Distributions in Statistical Ecology: One-Sample and Two-Sample Problems
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Purely Sequential and Two-Stage Fixed-Accuracy Confidence Interval Estimation Methods for Count Data from Negative Binomial Distributions in Statistical Ecology: One-Sample and Two-Sample Problems

机译：统计生态学中负二项分布的计数数据的纯连续和两阶段固定精度置信区间估计方法：一样本和两样本问题

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摘要

Our main focus is on count data arising from statistical ecology. Anscombe (1949) emphasized negative binomial (NB) modeling for overdispersed count data. A large majority of existing methodologies, both sequential and nonsequential, were reviewed by Mukhopadhyay and Banerjee (2012). We assume that the thatch parameter remains known and revisit a sequential confidence interval estimation method for an NB mean proposed by Willson and Folks (1983) that may not always guarantee a positive lower confidence limit. Moreover, any postsampling adjustment of their lower confidence limit would compromise the preset confidence coefficient. In this article, we provide an appropriate resolution by estimating the NB mean with a fixed-accuracy confidence interval such that both confidence limits are positive. Our proposed purely sequential and two-stage estimation methodologies enjoy asymptotic consistency and asymptotic efficiency properties. Next, we consider estimating the ratio of two NB means under a two-sample setup assuming that the thatch parameters remain known with equal sample sizes and provide both purely sequential and two-stage methodologies. These are shown to enjoy asymptotic consistency and asymptotic efficiency properties. Extensive sets of analyses based on both simulated data and real data from potato beetle infestation are presented to highlight some of the exciting small- and moderate-sample features of the proposed estimation methodologies.
机译：我们的主要重点是统计生态学产生的计数数据。 Anscombe（1949）强调了负二项式（NB）建模用于过度分散的计数数据。 Mukhopadhyay和Banerjee（2012）审查了绝大多数现有的方法学，包括顺序方法和非顺序方法。我们假设茅草参数仍然是已知的，并针对Willson和Folks（1983）提出的NB均值重新采用顺序置信区间估计方法，该方法可能并不总能保证正的较低置信区间。此外，对其下置信限的任何后采样调整都会损害预设的置信系数。在本文中，我们通过估计具有固定准确度置信区间的NB均值来提供适当的分辨率，以使两个置信限均为正值。我们提出的纯顺序和两阶段估计方法具有渐近一致性和渐近效率属性。接下来，我们假设在茅草参数保持已知且样本量相等的情况下，考虑在两个样本的设置下估算两个NB均值的比率，并提供纯序贯和两阶段方法。这些显示出具有渐近一致性和渐近效率特性。提出了基于模拟数据和马铃薯甲虫侵扰的真实数据的大量分析，以突出提出的估算方法的一些令人兴奋的中小样本特征。

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