发表机构
University Giustino Fortunato; Department of Mathematics, University of Trento（朱斯蒂诺·富尔纳托大学; 特伦托大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对p维环面多元圆形数据缺失问题，提出基于包裹椭圆对称分布族的EM算法进行参数估计与填补，通过蒙特卡洛模拟验证性能。
AI 中文摘要
本文针对p维环面上的多元圆形数据在存在缺失值时的参数估计与基于模型的填补问题。实际上，样本空间的周期性使得针对欧几里得数据设计的传统填补技术失效。为此，我们提出了一个在可忽略缺失机制下，基于包裹椭圆对称分布族进行最大似然估计的通用框架，特别关注多元包裹正态分布。该方法利用椭圆对称分布在展开空间上的条件性质，将缺失环形数据的填补嵌入到期望最大化（EM）算法中，该算法将包裹系数和缺失条目均视为潜在变量。文中详细推导了E步和M步，并讨论了一个可行的算法。同时，也考虑了填补方法。在包裹正态设定下，通过蒙特卡洛模拟评估了在可忽略缺失机制下最大似然估计的有限样本性能。该方法还在人为引入缺失的数据上进行了演示。
英文摘要
This paper addresses the problem of parameter estimation and model-based imputation for multivariate circular data lying on a p-dimensional torus in the presence of missing values. Actually, the periodic nature of the sample space invalidates conventional imputation techniques designed for Euclidean data. Then, we propose a general framework for maximum likelihood estimation under the wrapped elliptically symmetric family of distributions, with particular interest in the multivariate wrapped normal distribution, when the missing data mechanism is ignorable. The methodology leverages the conditional properties of the elliptically symmetric distributions on the unwrapped space, embedding the imputation of missing torus data into an Expectation-Maximization algorithm that treats both the wrapping coefficients and the missing entries as latent variables. Derivation of both the E and M steps is detailed and a working algorithm is discussed. Imputation methods are also taken into account. The finite-sample performance of the maximum likelihood estimator under ignorable missingness is assessed through Monte Carlo simulations under the wrapped normal specification. The methodology is also illustrated on data with artificially introduced missingness.
