Comparison of the Gamma kernel and the orthogonal series methods of density estimation

The standard kernel density estimator suffers from a boundary bias issue for probability density function of distributions on the positive real line. The Gamma kernel estimators and orthogonal series estimators are two alternatives which are free of boundary bias. In this paper, a simulation study is conducted to compare small-sample performance of the Gamma kernel estimators and the orthogonal series density estimator with Laguerre and Hermite basis. We found that if the basis function is chosen based on some partial knowledge about the shape of target density, then orthogonal series estimator can outperform the Gamma kernel estimator.