Kernel density estimation under widely orthant dependence

Abstract

The kernel density estimator for widely orthant dependent random variables is studied. The exponential inequalities and the exponential rate for the estimator of a density function with a uniform version over compact sets are investigated. Further, the consistency of the estimator is proved. The results are generalizations of some existing outcomes for both associated and negatively associated samples. The convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.