We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. (2014) 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. Real data illustrations are also included.