RT Generic
T1 Multivariate expectile trimming and the BExPlot
A1 Cascos Fernández, Ignacio
A1 Ochoa Arellano, Maicol Jesús
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB 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.
SN 2387-0303
YR 2019
FD 2019-05
LK https://hdl.handle.net/10016/28434
UL https://hdl.handle.net/10016/28434
LA eng
NO This research was partially supported by the Spanish Ministry of Science and Innovation under grant ECO2015-66593-P.
DS e-Archivo
RD 1 sept. 2024