Data Depth and Multiple Output Regression, the Distorted M -Quantiles Approach

Maicol Ochoa () and Ignacio Cascos ()
Additional contact information
Maicol Ochoa: Department of Statistics, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain
Ignacio Cascos: Department of Statistics, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain

Mathematics, 2022, vol. 10, issue 18, 1-19

Abstract: For a univariate distribution, its M -quantiles are obtained as solutions to asymmetric minimization problems dealing with the distance of a random variable to a fixed point. The asymmetry refers to the different weights awarded to the values of the random variable at either side of the fixed point. We focus on M -quantiles whose associated losses are given in terms of a power. In this setting, the classical quantiles are obtained for the first power, while the expectiles correspond to quadratic losses. The M -quantiles considered here are computed over distorted distributions, which allows to tune the weight awarded to the more central or peripheral parts of the distribution. These distorted M -quantiles are used in the multivariate setting to introduce novel families of central regions and their associated depth functions, which are further extended to the multiple output regression setting in the form of conditional and regression regions and conditional depths.

Keywords: bivariate depth algorithm; data depth; distortion function; M -quantiles; multiple output regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/18/3272/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/18/3272/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:18:p:3272-:d:910734

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().