Nonparametric Estimation of Possibly Similar Densities

Abstract

In empirical settings it is sometimes necessary to estimate a set of densities which are thought to be of similar structure. In a parametric framework, similarity may be imposed by assuming the densities belong to the same parametric family. A class of nonparametric methods, inspired by the work of Hjort and Glad (1995), is developed that offers greater efficiency if the set of densities is similar while seemingly not losing any if the set of densities are dissimilar. Both theoretical properties and €nite sample performance are found to be promising. The developed estimator is relatively easy to implement, does not require knowledge of the form or extent of any possible similarities, and may be combined with semiparametric and bias reduction methods.