Estimation of confidence intervals for the mean of heavy tailed loss distributions: a comparative study using a simulation method

This paper uses nonparametric methods to estimate the confidence intervals for the mean of asymmetric heavy tailed loss distributions. The nonparametric methods employed are the m out of n bootstrap, subsampling bootstrap, refined bootstrap, empirical likelihood ratio method, and bootstrap calibrated empirical likelihood methods. We evaluate the accuracy and compare the performance of the confidence interval estimates for the mean via a simulation study. In terms of the coverage probabilities, the results show that the m out of n bootstrap method performs well in samples of size 500 and 1000 and the empirical likelihood method performs well only in samples of size 1000.