WITHDRAWN: Direct Density Estimation of L-Estimates via Characteristic Functions with Applications

• Author(s): Dongliang Wang and Alan Hutson and Jeffrey Miecznikowski
• Keywords: Bootstrap ; nonparametric ; characteristic function

Abstract

In this note we develop a new and novel kernel density estimator for directly estimating the probability and cumulative distribution function of an L-estimate from a single population based on utilizing the theory in Knight (1985) in conjunction with classical inversion theory. The resulting estimator is "bootstrap-like" in terms of its properties with respect to the derivation of approximate confidence intervals via a "plug-in" approach. This new approach is distinct from the bootstrap methodology in that it is analytically and computationally feasible to provide an exact estimate of the distribution function through direct calculation. Thus our approach eliminates the error due to Monte Carlo resampling that arises within the context of simulation based approaches.