A family of asymmetric kernels based on log-symmetric distributions

Abstract

This paper proposes a class of asymmetric kernels based on log-symmetric (LS) distributions for probability density function estimation in the context of strictly positive skewed data. Some asymptotic properties (bias, variance and mean integrated squared error) of the LS kernel density estimators are established. The choice of bandwidth is investigated by adapting the rule-of-thumb and cross-validation methods. A simulation study investigates the performance of the proposed LS kernel density estimators and compare their performances with the Kakizawa’s LS kernel estimators [Nonparametric density estimation for nonnegative data, using symmetrical-based inverse and reciprocal inverse Gaussian kernels through dual transformation. Journal of Statistical Planning and Inference. 2018; 193:117–135]. Finally, an application on real data is analyzed.