Penalized smoothing of sparse tables

Abstract

In models using categorical data one may use some adjacency relations to justify the use of smoothing to improve upon simple histogram approximations of the probabilities. This is particularly convenient when in presence of a sparse number of observations. Moreover, in many models, the prior knowledge of a marginal distribution is available. We propose two families of polynomial smoothers that incorporate this marginal information into the estimates. Besides, one of the family, the penalized polynomial smoothers, corrects the well known drawback of the polynomial smoothers of producing negative approximations. A simulation study show a good performance of the proposed estimators with respect to usual error criteria. Our estimators, and particularly the penalized family, perform especially well for sparse situations.