 Expectile depth: Theory and computation for bivariate datasetsIgnacio Cascos and Maicol Ochoa Journal of Multivariate Analysis, 2021, vol. 184, issue C Abstract: Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble the quantiles, and just like them, expectiles are indexed by a level α in the unit interval. In the present paper, we introduce and discuss the main properties of the (multivariate) expectile regions, a nested family of sets, whose instance with level 0<α≤1∕2 is built up by all points whose univariate projections lie between the expectiles of levels α and 1−α of the projected dataset. Such level is interpreted as the degree of centrality of a point with respect to a multivariate distribution and therefore serves as a depth function. We propose here algorithms for determining all the extreme points of the bivariate expectile regions as well as for computing the depth of a point in the plane. We also study the convergence of the sample expectile regions to the 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) is introduced. Keywords: Algorithm; Bagplot; Data depth; Depth region; Expectile (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x2100035x Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2021.104757 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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