Geodesic
Transformations to symmetry based on the probability weighted characteristic function
Kybernetika, Tome 51 (2015) no. 4, pp. 571-587.

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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.
DOI : 10.14736/kyb-2015-4-0571
Classification : 62G10, 62G20
Keywords: characteristic function; empirical characteristic function; probability weighted moments; symmetry transformation 
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Meintanis, Simos G.; Stupfler, Gilles. Transformations to symmetry based on the probability weighted characteristic function. Kybernetika, Tome 51 (2015) no. 4, pp. 571-587. doi : 10.14736/kyb-2015-4-0571. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0571/

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