Meintanis, Simos G.Stupfler, Gilles2016-09-062016-09-062015Meintanis, S.G. & Stupfler, G. 2015. Transformations to symmetry based on the probability weighted characteristic function. Kybernetika, 51(4):571-587. [http://dx.doi.org/10.14736/kyb-2015-4-0571]0023-5954 (Online)http://hdl.handle.net/10394/18548http://dx.doi.org/10.14736/kyb-2015-4-0571http://www.kybernetika.cz/content/2015/4/571We 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 includedenCharacteristic functionempirical characteristic functionprobability weighted momentssymmetry transformationArticle