Empirical Likelihood Based Asymmetric Kernel Estimation Method And Its Application

The estimation of actuarial loss function is one of the most important re-search content in actuarial science, especially the estimation of the density at the tail. The estimation of the tail will largely affect the application in practice. So how to produce a estimation finely reflecting the characteristics of the loss data is the key to solve this puzzle. Traditional symmetric kernel estimation method proposed by some scholars has better performance then parametric model and histogram, but it suffers from boundary bias, lack of local adaptivity, and the tendency to flatten out peaks and valleys of true density. We propose a non-parametric method which combines asymmetric kernel and empirical likelihood .This non-parametric method makes the density estimation has the same moment or quintile with the data by constructing estimating equations,which reproduce the sample weights instead of the n-1 in the traditional estimation. Our density estimation is also free of boundary bias and has better local adaptivity. Then we prove consistency of the new method. Finally, we compare our new method with competing methods in estimating actuarial loss function both in simulation and practical data study. The simulation results show that the density estimation using the new method matches the true density more closely then the competing methods.