分析逐元加权数据
Analyzing cellwise weighted data
AI总结：
针对数据矩阵各单元格带权的情形，本文提出基于解包变换的逐元加权似然框架，支持最大似然估计、似然比检验和协方差矩阵估计，并给出R实现及渐近等价的快速近似方法。
摘要：
数据集的行（个案、对象）通常带有权重。例如，一个个案的权重可以反映它被观测到的次数，或其可靠性。为分析这类数据，已有许多逐行加权技术，其中最著名的是加权平均。但也存在数据矩阵中各个单元格（条目）被赋予权重的情形。本札记的目的是提供一种分析此类数据的方法。我们定义了逐元加权似然函数，它对应于对数据集的一种变换，我们称之为解包。利用该加权似然，可以开展最大似然估计和似然比检验等多元统计方法。我们特别关注协方差矩阵的估计，因为协方差矩阵是大量多元统计方法的构建模块。文中提供了逐元最大似然估计量的R实现，该实现采用了一个版本的EM算法。此外还提出了一种更快的近似方法，该方法与其渐近等价。
英文摘要：
Often the rows (cases, objects) of a dataset have weights. For instance, the weight of a case may reflect the number of times it has been observed, or its reliability. For analyzing such data many rowwise weighted techniques are available, the most well known being the weighted average. But there are also situations where the individual cells (entries) of the data matrix have weights assigned to them. The purpose of this note is to provide an approach to analyze such data. We define a cellwise weighted likelihood function, that corresponds to a transformation of the dataset which we call unpacking. Using this weighted likelihood one can carry out multivariate statistical methods such as maximum likelihood estimation and likelihood ratio tests. We pay particular attention to the estimation of covariance matrices, because these are the building blocks of much of multivariate statistics. An R implementation of the cellwise maximum likelihood estimator is provided, which employs a version of the EM algorithm. Also a faster approximate method is proposed, which is asymptotically equivalent to it.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
