Multivariate expectile trimming and the BExPlot

  1. Cascos Fernández, Ignacio 1
  2. Ochoa Arellano, Maicol Jesús 1
  1. 1 Universidad Carlos III de Madrid
    info

    Universidad Carlos III de Madrid

    Madrid, España

    ROR https://ror.org/03ths8210

Revista:
Working paper Statistics and Econometrics

ISSN: 2387-0303

Año de publicación: 2019

Páginas: 33

Tipo: Documento de Trabajo

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Otras publicaciones en: Working paper Statistics and Econometrics

Resumen

Expectiles are the solution to an asymmetric least squares minimization problem forunivariate data. They resemble some similarities with the quantiles, and just like them,expectiles are indexed by a level α. In the present paper, we introduce and discussthe main properties of the expectile multivariate trimmed regions, a nested family ofsets, whose instance with trimming level α is built up by all points whose univariateprojections lie between the expectiles of levels α and 1 − α of the projected dataset.Such trimming level is interpreted as the degree of centrality of a point with respect toa multivariate distribution and therefore serves as a depth function. We study here theconvergence of the sample expectile trimmed regions to the population ones and theuniform consistency of the sample expectile depth. We also provide efficient algorithmsfor determining the extreme points of the expectile regions as well as for computing thedepth of a point in R2. These routines are based on circular sequence constructions.Finally, we present some real data examples for which the Bivariate Expectile Plot(BExPlot) is introduced.

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