On constrained estimation problems in time-use surveys

In the context of “stylized” time-use surveys, constrained estimation problems are common, a simple illustration being the constraint that the hours reported for a mutually exclusive and exhaustive set of activities in a given day should sum up to 24. An example is developed, using mixtures of multivariate normal models, which demonstrates that model-based inference can lead to estimators that can decisively outperform ad hoc strategies such as “shrinking towards the constraint” that have been recommended in the literature.