论文标题
椭圆形的对称分布，用于任意维度的定向数据
Elliptically symmetric distributions for directional data of arbitrary dimension
论文作者
论文摘要
我们制定了一类角度高斯分布，该分布允许不同程度的各向同性拷贝用于任意维度的定向随机变量。通过一系列新型的重新聚集化，该分布家族的索引是由具有有意义的统计解释的参数索引，可以在足够维度的整个真实空间中进行范围。新的参数化大大简化了所有模型参数的最大似然估计，这又导致理论上声音和数值稳定的推理过程，以推断分布的关键特征。来自基于可能性的推理的副产品用于开发图形和数值诊断工具，以评估数据应用程序中此分布的拟合优度。模拟研究和对水文地质研究数据的应用用于证明推理程序和诊断方法的实施和性能。
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by parameters with meaningful statistical interpretations that can range over the entire real space of an adequate dimension. The new parameterization greatly simplifies maximum likelihood estimation of all model parameters, which in turn leads to theoretically sound and numerically stable inference procedures to infer key features of the distribution. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.
