Expectile depth: Theory and computation for bivariate datasets

JOURNAL OF MULTIVARIATE ANALYSIS

卷:184

Article

Cascos, Ignacio¹  Ochoa, Maicol¹ 

[1] Univ Carlos III Madrid, Dept Stat, Madrid, Spain

关键词: Algorithm;    Bagplot;    Data depth;    Depth region;    Expectile;   

DOI  :  10.1016/j.jmva.2021.104757

来源: Elsevier

【 摘 要 】

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 a 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 < alpha <= 1/2 is built up by all points whose univariate projections lie between the expectiles of levels alpha and 1 - alpha 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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