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Uniform strong consistency of a frontier estimator using kernel regression on high order moments

Stéphane Girard;  Armelle Guillou;  Gilles Stupfler — 2014

ESAIM: Probability and Statistics

We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

Transformations to symmetry based on the probability weighted characteristic function

Simos G. Meintanis;  Gilles Stupfler — 2015

Kybernetika

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.

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