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首页> 外文期刊>Journal of statistical computation and simulation >Testing equality of two negative binomial means in presence of unequal over-dispersion parameters: a Behrens-Fisher problem analog
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Testing equality of two negative binomial means in presence of unequal over-dispersion parameters: a Behrens-Fisher problem analog

机译：在存在不相等的过度分散参数的情况下测试两个负二项式均值的相等性：Behrens-Fisher问题类似物

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Two samples count data with unequal over-dispersions arise in many applied statistics problems (biostatistics, epidemiology, etc.). In this situation, it is of interest to test the equality of the means. The traditional Behrens-Fisher problem is to test the equality of the means mu(1) and mu(2) of two normal populations where the variances sigma(2)(1) and sigma(2)(2) are unknown. The purpose of this paper is to deal with the corresponding problem for over-dispersed count data. We develop six test procedures, namely, a likelihood ratio test LR, a likelihood ratio test based on the bias corrected maximum likelihood estimates of the nuisance parameters LR(bc), a score test T-2, a score test based on the bias corrected estimates of the nuisance parameters T-2 (bc), a C(alpha) test based on the method of moments estimates of the nuisance parameters T-1 with Welch's [The significance of the difference between two means when the population variances are unequal. Biometrika. 1937;29:350-362] degree of freedom correction, and a test T-N using the asymptotic normal distribution of T-1. These procedures are then compared in terms of size and power using simulations. Simulations show the best overall performance of the statistic T-1 in terms of size and power and it is easy to calculate. For large sample sizes, for example, for n(1)=n(2)=50, all six statistics do well in terms of level and their power performances are also similar. So, for large sample sizes, the statistic T-N should be used as it is very easy to use in practice.
机译：在许多应用统计问题（生物统计学，流行病学等）中，两个样本计数的数据具有不相等的过度分散。在这种情况下，测试手段的均等性很有意义。传统的Behrens-Fisher问题是检验方差sigma（2）（1）和sigma（2）（2）未知的两个正态总体的均值mu（1）和mu（2）是否相等。本文的目的是要解决计数数据过度分散的相应问题。我们开发了六个测试程序，即似然比测试LR，基于偏差校正的扰动参数LR（bc）的最大似然估计的似然比测试，得分测试T-2，基于偏差校正的得分测试扰动参数T-2（bc）的估计值，这是一种基于Welch的矩量估计方法对扰动参数T-1进行矩估计的Cα测试[当总体方差不相等时，两种方法之间的差异的意义。 Biometrika。 1937; 29：350-362]自由度校正，并使用T-1的渐近正态分布测试T-N。然后使用仿真在大小和功耗方面比较这些过程。仿真显示，就大小和功效而言，统计T-1的总体性能最佳，并且易于计算。对于较大的样本量（例如，对于n（1）= n（2）= 50），所有六个统计量的水平都很好，并且它们的功效也相似。因此，对于大样本量，应使用统计量T-N，因为它在实践中非常容易使用。

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