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.

翻译：数据集的行( 大小写、 对象) 往往具有权重。 例如, 案例的权重可能反映观察到的数据次数或可靠性。 在分析这类数据时, 可以使用许多行式加权技术, 最著名的是加权平均值。 但是, 也有些情况下, 数据矩阵的单个单元格( 内) 有分配给它们的权重。 本说明的目的是提供一种分析这些数据的方法。 我们定义了一种小单元格加权概率功能, 与我们称之为解包的数据集转换相对应。 使用这种加权概率, 一个人可以采用多种变量统计方法, 如最大概率估计和概率比重测试。 我们特别注意对变量矩阵的估计, 因为这些是多变量统计的很多构件。 提供了使用单元格最大可能性的估算符, 从而使用一种 EM 算法的版本。 另外, 提出了一种快速的近似方法, 与该方法基本相同 。