用于高维多变量循环数据的多变量非负三角和分布
Multivariate Nonnegative Trigonometric Sums Distributions for High-Dimensional Multivariate Circular Data
AI总结：
本文完善基于非负三角和的多变量循环分布，阐明其边际化、条件化与独立性运算，并提出面向高维数据的拟合优度检验和参数估计算法。
摘要：
Fernández-Durán 和 Gregorio-Domínguez（2014）通过考虑多个非负三角和，定义了一族针对循环随机变量向量的概率分布。这些分布具有高度灵活性，并可呈现众多众数和偏度。对这些多变量分布的若干运算被转化为对参数向量的运算；例如，边缘化涉及计算矩阵的特征向量和特征值，而循环变量向量各子集之间的独立性则转化为参数向量相应子集的 Kronecker 积。此外，文中证明了基于非负三角和的多变量循环分布族在边缘化和条件化下是封闭的，也就是说，任意阶的边际密度和条件密度同样属于该分布族。在将该模型实际应用于真实数据集时，从联合多变量密度推导边际密度和条件密度十分重要。文中提出了一种基于特征函数的拟合优度检验，以及一种用于高维循环数据的替代参数估计算法，并将其应用于一个关于金融市场价格最大值和最小值每日发生时刻的真实数据集。
英文摘要：
Fernández-Durán and Gregorio-Domínguez (2014) defined a family of probability distributions for a vector of circular random variables by considering multiple nonnegative trigonometric sums. These distributions are highly flexible and can present numerous modes and skewness. Several operations on these multivariate distributions were translated into operations on the vector of parameters; for instance, marginalization involves calculating the eigenvectors and eigenvalues of a matrix, and independence among subsets of the vector of circular variables translates to a Kronecker product of the corresponding subsets of the vector of parameters. Furthermore, it was demonstrated that the family of multivariate circular distributions based on nonnegative trigonometric sums is closed under marginalization and conditioning, that is, the marginal and conditional densities of any order are also members of the family. The derivation of marginal and conditional densities from the joint multivariate density is important when applying this model in practice to real datasets. A goodness-of-fit test based on the characteristic function and an alternative parameter estimation algorithm for high-dimensional circular data was presented and applied to a real dataset on the daily times of occurrence of maxima and minima of prices in financial markets.
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