  Nowadays, the confidentiality of data and information is of great importance
for many companies and organizations. For this reason, they may prefer not to
release exact data, but instead to grant researchers access to approximate
data. For example, rather than providing the exact measurements of their
clients, they may only provide researchers with grouped data, that is, the
number of clients falling in each of a set of non-overlapping measurement
intervals. The challenge is to estimate the mean and variance structure of the
hidden ungrouped data based on the observed grouped data. To tackle this
problem, this work considers the exact observed data likelihood and applies the
Expectation-Maximization (EM) and Monte-Carlo EM (MCEM) algorithms for cases
where the hidden data follow a univariate, bivariate, or multivariate normal
distribution. Simulation studies are conducted to evaluate the performance of
the proposed EM and MCEM algorithms. The well-known Galton data set is
considered as an application example.
