Nonparametric Estimation of Distributions in Random Effects Models

We propose using minimum distance to obtain nonparametric estimates of the distributions of components in random effects models. A main setting considered is equivalent to having a large number of small data sets whose locations and scales vary randomly, but which otherwise have a common distribution. Interest focuses on estimating the distribution that is common to all data sets, although methods for estimating the distribution of location and scale are also addressed. The former distribution is crucial in multiple testing problems where one wishes to apply a location/scale invariant test to every small data set. A detailed algorithm for computing minimum distance estimates is proposed, and the usefulness of our methodology is illustrated by a simulation study and an analysis of microarray data.