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Interval estimation of gamma for an R x S table

机译：R x S表的伽马间隔估计

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When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited. Because it is well known that an interval estimator using Wald's statistic is generally not likely to perform well especially when the sample size is small, the goal of this paper is to find ways to improve the finite-sample performance of this estimator. This paper develops five asymptotic interval estimators of the gamma by employing various methods that are commonly used to improve the normal approximation of the maximum likelihood estimator (MLE). Using Monte Carlo simulation. this paper notes that the coverage probability of the interval estimator using Wald's statistic can be much less than the desired confidence level, especially when the underlying gamma is large. Further, except for the extreme case, in which the underlying gamma is large and the sample size is small, the interval estimator using a logarithmic transformation together with a monotonic function proposed here not only performs well with respect to the coverage probability, but is also more efficient than all the other estimators considered here. Finally, this paper notes that applying an ad hoe adjustment procedure whenever any observed frequency equals 0, we add 0.5 to all cells in calculation of the cell proportions can substantially improve the traditional interval estimator. This paper includes two examples to illustrate the practical use of interval estimators considered here.
机译：当基本响应在序数尺度上时，伽玛是衡量两个有序变量之间关联强度的最常用指标之一。但是，除了简要介绍基于Wald统计量的传统区间估计器的使用以外，对伽玛区间估计的讨论也受到限制。因为众所周知，使用Wald统计量的区间估计器通常不太可能表现良好，尤其是在样本量较小的情况下，因此，本文的目标是寻找提高该估计器有限样本性能的方法。本文通过采用通常用于改善最大似然估计器（MLE）的正常逼近的各种方法，开发了五个伽玛的渐近区间估计器。使用蒙特卡洛模拟。本文指出，使用Wald统计量的区间估计量的覆盖率可能远小于所需的置信度，尤其是当基础伽玛较大时。此外，除了基本伽玛值大且样本量较小的极端情况外，使用对数变换和此处提出的单调函数的区间估计器不仅在覆盖率方面表现良好，而且比这里考虑的所有其他估算器更有效。最后，本文指出，只要观察到的频率等于0，就采用adhoe调整程序，在计算单元比例时，对所有单元加0.5，可以大大改善传统的间隔估计器。本文包括两个示例，以说明此处考虑的区间估计器的实际使用。

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