Test statistics derived as components of Pearson's phi-squared distance measure
Test statistics derived as components of Pearson's phi-squared distance measure
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作为皮尔逊 phi 平方距离度量的组成部分导出的检验统计量
DOI：
10.1080/01621459.1987.10478503
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发表时间：
1987
影响因子：
3.7
通讯作者：
R. Rosenstein
中科院分区：
文献类型：
--
作者：
R. Eubank;V. LaRiccia;R. Rosenstein
摘要基于Pearson θ2测度，提出了两个绝对连续分布比较的一般方法。虽然θ2没有简单的估计，但它可以分解成各个分量，所有的分量都很容易估计。导出了分量估计的渐近分布理论，并考虑了若干标准问题的分量形式。结果表明，分量-θ - 2方法为开发各种问题的测试提供了统一的方法，并且对于生成新的测试程序很有用。θ2的分量方法是基于所谓的比较密度。即给定密度为F和H的两个绝对连续分布F和H，比较密度定义为d(u) = F (H -1 (u))/ H (H -1 (u))，其中H -1为H分位数函数。由于在假设F = H下d必须是一致的，因此φ2 =∫10 (d(u)−1)2 du提供了对假设有效性的总体度量。通过u…
Abstract A general approach to the comparison of two absolutely continuous distributions is presented based on Pearson's θ2 measure. Although no simple estimates are available for θ2, it can be decomposed into components, all of which are easily estimated. Asymptotic distribution theory is derived for the component estimates, and the form of the components is considered for several standard problems. It is demonstrated that the components-of-θ2 approach provides a unified approach to the development of tests for a variety of problems and that it is useful for generating new test procedures. The components-of-θ2 approach is based on what is termed a comparison density. That is, given two absolutely continuous distributions F and H with densities f and h, the comparison density is defined as d(u) = f(H –1(u))/h(H –1(u)), where H –1 is the H quantile function. Since d must be uniform under the hypothesis F = H, an overall measure of the validity of the hypothesis is provided by φ2 = ∫1 0 (d(u) − 1)2 du. By u...