A new distribution function estimator based on a nonparametric transformation of the data with applications

Abstract

The purpose of this study is to investigate the properties of a bias reduction kernel estimator of a distribution function and to compare it with existing estimation techniques in the bootstrap. The procedure which is to be investigated, was proposed by Swanepoel and van Gram (2003). Monte Carlo simulation studies were performed to compare this procedure with existing procedures in the bootstrap methodology. The simulations involved constructing 90% and 95% two-sided percentile confidence intervals and upper bounds for the mean. The simulation study provided estimates for the coverage probabilities and expected lengths of the intervals. Findings and conclusions of these simulations are reported.