Density estimation using inverse and reciprocal inverse Gaussian kernels

This paper introduces two new nonparametric estimators for probability density functions which have support on the non-negative real line. These kernel estimators are based on some inverse Gaussian (IG) and reciprocal inverse Gaussian (RIG) probability density functions used as kernels. We show that they share the same properties as those of gamma kernel estimators: they are free of boundary bias, always non-negative and achieve the optimal rate of convergence for the mean integrated squared error (MISE). Monte Carlo results concerning finite sample properties are reported for different distributions and sample sizes.