Transformations to symmetry based on the probability weighted characteristic function

Abstract

We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite{sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included