论文标题
非归一化离散概率分布及其在统计中的应用的表征
Characterizations of non-normalized discrete probability distributions and their application in statistics
论文作者
论文摘要
从Stein方法核心的分布特征中，我们为识别这些分布的离散概率定律的质量函数提供了明确的公式。这些身份用于开发解决统计问题的工具。我们的特征，因此，构建的应用程序不需要有关概率法律的正常化常数的任何知识。为了证明我们的统计方法是合理的，我们提供了比较模拟研究，以测试对泊松分布的拟合，以及当两个参数尚不清楚时，为负二项式家族的参数估计。我们还考虑了通常非归一化的离散指数 - 分解模型的参数估计问题。
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.
