  With contemporary data sets becoming too large to analyze the data directly,
various forms of aggregated data are becoming common. The original individual
data are points, but after aggregation, the observations are interval-valued
(e.g.). While some researchers simply analyze the set of averages of the
observations by aggregated class, it is easily established that approach
ignores much of the information in the original data set. The initial
theoretical work for interval-valued data was that of Le-Rademacher and Billard
(2011), but those results were limited to estimation of the mean and variance
of a single variable only. This article seeks to redress the limitation of
their work by deriving the maximum likelihood estimator for the all important
covariance statistic, a basic requirement for numerous methodologies, such as
regression, principal components, and canonical analyses. Asymptotic properties
of the proposed estimators are established. The Le-Rademacher and Billard
results emerge as special cases of our wider derivations.
