Relative smoothing of discrete distributions with sparse observations

Abstract

Quite often we are faced with a sparse number of observations over a finite number of cells and are interested in estimating the cell probabilities. Some local polynomial smoothers or local likelihood estimators have been proposed to improve on the histogram, which would produce too many zero values. We propose a relativized local polynomial smoothing for this problem, weighting heavier the estimating errors in small probability cells. A simulation study about the estimators that are proposed show a good behaviour with respect to natural error criteria, especially when dealing with sparse observations.