Kernel estimation of residual extropy function under α-mixing dependence condition

Abstract

As in the context of introducing the concept of residual entropy in the literature, Qiu and Jia (2018b) introduced the concept, residual extropy to measure the residual uncertainty of a random variable. In this work, we propose a nonparametric estimator for the residual extropy, where the observations under consideration are exhibiting α-mixing (strong mixing) dependence condition. Asymptotic properties of the estimator is derived under suitable regular conditions. A Monte Carlo simulation study is carried out to evaluate the performance of the estimator using the mean squared errors.