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research-article

Expectile depth: : Theory and computation for bivariate datasets

Authors:

Ignacio Cascos,

Maicol OchoaAuthors Info & Claims

Volume 184, Issue C

https://doi.org/10.1016/j.jmva.2021.104757

Published: 01 July 2021 Publication History

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.

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Cited By

Daouia AStupfler GUsseglio-Carleve A(2024)An expectile computation cookbookStatistics and Computing10.1007/s11222-024-10403-x34:3Online publication date: 23-Mar-2024
https://dl.acm.org/doi/10.1007/s11222-024-10403-x

Index Terms

Expectile depth: Theory and computation for bivariate datasets
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
  2. Probability and statistics
    1. Statistical paradigms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
    2. Mathematical optimization

Index terms have been assigned to the content through auto-classification.

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Information

Published In

cover image Journal of Multivariate Analysis

Journal of Multivariate Analysis Volume 184, Issue C

Jul 2021

331 pages

ISSN:0047-259X

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Elsevier Inc.

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 July 2021

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Cited By

Daouia AStupfler GUsseglio-Carleve A(2024)An expectile computation cookbookStatistics and Computing10.1007/s11222-024-10403-x34:3Online publication date: 23-Mar-2024
https://dl.acm.org/doi/10.1007/s11222-024-10403-x

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