Estimating the density and hazard rate functions using the reciprocal inverse Gaussian kernel

Abstract

In this paper, we use the Reciprocal Inverse Gaussian (RIG) kernel to estimate nonparametrically the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The estimator uses adaptive weights depending on the points at which we estimate the functions. We derive the strong consistency, the asymptotic normality and the asymptotic mean squared error (AMSE) of the proposed estimator. Also, the selection of the optimal bandwidth is investigated. The performance of the proposed estimator is compared to that of the Gaussian kernel.