Identifiability of asymmetric circular and cylindrical distributions
Identifiability of asymmetric circular and cylindrical distributions
复制标题
非对称圆形和圆柱形分布的可识别性
DOI：
10.1007/s13171-022-00294-3
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Miyata;Y.;Shiohama;T.;and Abe;T.
统计模型的可辨识性是证明极大似然估计相合性的一个基本和必要条件。在文献中，还没有充分研究用于估计模型参数的圆形和圆柱体上的偏态分布族的可识别性。本文提出了一种结合三角矩和同时丢番图逼近的新方法，证明了非对称圆分布和圆柱分布的可识别性。利用这种方法，我们证明了一般正弦偏态圆分布（包括正弦偏态von Mises分布和正弦偏态包裹Cauchy分布）和Möbius变换心形分布（可视为单位圆上的非对称分布）的可辨识性。此外，我们还证明了两个圆柱分布的可识别性，其中圆形随机变量的两个边缘分布都是正弦偏态包裹柯西分布，而给定圆形随机变量，随机变量在非负真实的直线上的条件分布分别是威布尔分布和广义Pareto型分布.
Identifiability of statistical models is a fundamental and essential condition that is required to prove the consistency of maximum likelihood estimators. The identifiability of the skew families of distributions on the circle and cylinder for estimating model parameters has not been fully investigated in the literature. In this paper, a new method combining the trigonometric moments and the simultaneous Diophantine approximation is proposed to prove the identifiability of asymmetric circular and cylindrical distributions. Using this method, we prove the identifiability of general sine-skewed circular distributions, including the sine-skewed von Mises and sine-skewed wrapped Cauchy distributions, and that of a Möbius transformed cardioid distribution, which can be regarded as asymmetric distributions on the unit circle. In addition, we prove the identifiability of two cylindrical distributions wherein both marginal distributions of a circular random variable are the sine-skewed wrapped Cauchy distribution, and conditional distributions of a random variable on the non-negative real line given the circular random variable are a Weibull distribution and a generalized Pareto-type distribution, respectively.