Density Estimation of a Unimodal Continuous Distribution in the Presence of Outliers

Abstract

The “forward search” (FS) is a powerful general method for identifying outliers and their effects on the fitted model. The present study investigates the implementation of the FS method to identify outliers in nonparametric univariate density estimation framework, where the training sample is from a unimodal continuous distribution. The performance of this procedure has been illustrated by some simulation studies and real data examples. It is shown that outliers can lead to unsuitable estimation of a density function. When the number of outliers relative to the number of all observations is small, determination and elimination of the outliers can fit a reasonable density function to a dataset. Finally, it is shown that the simple ordering system proposed in this article can be used in some other frameworks.