Relating Quantiles and Expectiles Under Weighted-Symmetry

Recently, quantiles and expectiles of a regression function have been investigated by several authors. In this work, we give a sufficient condition under which a quantile and an expectile coincide. We extend some classical results known for mean, median and symmetry to expectiles, quantiles and weighted-symmetry. We also study split-models and sample estimators of expectiles. 1 Supported in part by the Fonds Institutionnel de Recherche, Universit'e du Qu'ebec `a Trois-Rivi`eres and by the Natural Sciences and Engineering Research Council of Canada, Grant No. OGP0089787. 2 Supported in part by the Fonds Institutionnel de Recherche, Universit'e du Qu'ebec `a Trois-Rivi`eres and by the Natural Sciences and Engineering Research Council of Canada, Grant No. OGP0042137. Key words and phrases : Quantiles, expectiles, weighted-symmetry, split-models. AMS 1990 subject classifications: Primary 62G05; secondary . Quantiles, expectiles and weigthed-symmetry 2 1 INTRODUCTION Given an explana..