Transformations to symmetry based on the probability weighted characteristic function

Simos Meintanis (1) , Gilles Stupfler (2)

1 NKUA - National and Kapodistrian University of Athens
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

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.

Domaines: Applications [stat.AP]; Mathématiques [math]

Simos Meintanis, Gilles Stupfler. Transformations to symmetry based on the probability weighted characteristic function. 2014. ⟨hal-01018575v2⟩