Varying kernel density estimation on R+R+

In this article a new nonparametric density estimator based on the sequence of asymmetric kernels is proposed. This method is natural when estimating an unknown density function of a positive random variable. The rates of Mean Squared Error, Mean Integrated Squared Error, and the L1L1-consistency are investigated. Simulation studies are conducted to compare a new estimator and its modified version with traditional kernel density construction.