We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis {\it 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.