几种常见概率规律的矩估计和综合卡方检验
Moments estimators and omnibus chi-square tests for some usual probability laws
摘要：
对于许多概率定律，在参数模型中，参数的估计可以在极大似然方法的框架中进行，或者在矩估计方法的框架中进行，或者通过使用插入方法等。通常，对于估计多个参数，使用相同的框架。本文重点研究矩估计方法。我们使用Lo（2016）中的函数经验过程（fep）工具来展示如何以几乎代数的方式推导出联合分布高斯定律并从中推导出综合卡方渐进定律。我们选择了四个分布来说明该方法（Gamma定律，Beta定律，Uniform定律和Fisher定律），并尽可能完整地描述矩估计量的渐近定律。进行模拟研究，以调查每种情况下获得的统计检验可验证的最小尺寸。一般来说，这里提出的综合卡方检验在样本量为50左右时效果良好
英文摘要：
For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for estimating more than one parameter, the same frame is used. We focus on the moment estimation method in this paper. We use the instrumental tool of the functional empirical process (fep) in Lo (2016) to show how it is practical to derive, almost algebraically, the joint distribution Gaussian law and to derive omnibus chi-square asymptotic laws from it. We choose four distributions to illustrate the method (Gamma law, beta law, Uniform law and Fisher law) and completely describe the asymptotic laws of the moment estimators whenever possible. Simulations studies are performed to investigate for each case the smallest sizes for which the obtained statistical tests are recommendable. Generally, the omnibus chi-square test proposed here work fine with sample sizes around fifty
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