  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.
