Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the log-likelihood function involves an infinite sum of indices in \({\mathbb {Z}}^p\), where p is the dimension of the data. To overcome this problem, for moderate dimension p, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.

在使用诸如指南针，量角器，风向标，六分仪或经纬仪等仪器的领域中，多变量圆形观测（即圆环上的点）经常出现。多元包装模型通常适合描述散布在p维环面上的数据点。但是，基于这种模型的统计推断相当复杂，因为对数似然函数中的每个贡献都涉及\（{{mathbb {Z}} ^ p \）中的索引的无限和，其中p是数据的维数。为了克服这个问题，对于中等尺寸p，我们提出了两种基于期望最大化和分类期望最大化算法的估计程序。我们在蒙特卡洛模拟上研究了提出的技术的性能，并进一步说明了在三个真实数据集上的新程序的优势。