An expectile computation cookbook

Abdelaati Daouia, Gilles Stupfler and Antoine Usseglio-Carleve
Additional contact information
Abdelaati Daouia: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Antoine Usseglio-Carleve: MATHSTIC - SFR UA MathSTIC - UA - Université d'Angers, LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: A substantial body of work in the last 15 years has shown that expectiles constitute an excellent candidate for becoming a standard tool in probabilistic and statistical modeling. Surprisingly, the question of how expectiles may be efficiently calculated has been left largely untouched. We fill this gap by, first, providing a general outlook on the computation of expectiles that relies on the knowledge of analytic expressions of the underlying distribution function and mean residual life function. We distinguish between discrete distributions, for which an exact calculation is always feasible, and continuous distributions, where a Newton-Raphson approximation algorithm can be implemented and a list of exceptional distributions whose expectiles are in analytic form can be given. When the distribution function and/or the mean residual life is difficult to compute, Monte-Carlo algorithms are introduced, based on an exact calculation of sample expectiles and on the use of control variates to improve computational efficiency. We discuss the relevance of our findings to statistical practice and provide numerical evidence of the performance of the considered methods.

Keywords: Control variates; Exact computation; Expectiles; Monte-Carlo sampling; Newton-Raphson method; Quadratic convergence (search for similar items in EconPapers)
Date: 2024
Note: View the original document on HAL open archive server: https://hal.science/hal-04524319v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Statistics and Computing, 2024, 34, pp.103. ⟨10.1007/s11222-024-10403-x⟩

Downloads: (external link)
https://hal.science/hal-04524319v1/document (application/pdf)

Related works:
Working Paper: An expectile computation cookbook (2023)
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:hal:journl:hal-04524319

DOI: 10.1007/s11222-024-10403-x

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().