Nonparametric density estimation for nonnegative data, using symmetrical-based inverse and reciprocal inverse Gaussian kernels through dual transformation

The classical Birnbaum-Saunders (BS) distribution has recently been generalized in various ways to introduce flexible parametric models for nonnegative data, focusing on the parametric fitting. In this paper, a new symmetrical-based inverse/reciprocal inverse Gaussian density, through dual transformation, is applied to the context of nonparametric density estimation for nonnegative data. The beauty and importance of new density estimator lies in its general formulation via the density generator, including a log-symmetrical kernel density estimator. We provide sufficient conditions under which the proposed estimator has desirable asymptotic properties, and discuss the asymptotic comparison between the proposed estimator and the previous (normal-based) estimator.