RT Journal Article
T1 Expectile depth: Theory and computation for bivariate datasets
A1 Cascos Fernández, Ignacio
A1 Ochoa Arellano, Maicol Jesús
AB Expectiles are the solution to an asymmetric least squares minimization problem forunivariate data. They resemble the quantiles, and just like them, expectiles are indexedby a level α in the unit interval. In the present paper, we introduce and discuss the mainproperties of the (multivariate) expectile regions, a nested family of sets, whose instancewith level 0 < α ≤ 1/2 is built up by all points whose univariate projections lie betweenthe expectiles of levels α and 1 − α of the projected dataset. Such level is interpretedas the degree of centrality of a point with respect to a multivariate distribution andtherefore serves as a depth function. We propose here algorithms for determining allthe extreme points of the bivariate expectile regions as well as for computing the depthof a point in the plane. We also study the convergence of the sample expectile regions tothe population ones and the uniform consistency of the sample expectile depth. Finally,we present some real data examples for which the Bivariate Expectile Plot (BExPlot) isintroduced.
PB Elsevier
SN 0047-259X
YR 2021
FD 2021-07-01
LK https://hdl.handle.net/10016/34168
UL https://hdl.handle.net/10016/34168
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 7 ago. 2024