IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03181017.html
   My bibliography  Save this paper

Extremile regression

Author

Listed:
  • 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)

  • Irene Gijbels
  • Gilles Stupfler

Abstract

Regression extremiles define a least squares analogue of regression quantiles. They are determined by weighted expectations rather than tail probabilities. Of special interest is their intuitive meaning in terms of expected minima and maxima. Their use appears naturally in risk management where, in contrast to quantiles, they fulfill the coherency axiom and take the severity of tail losses into account. In addition, they are comonotonically additive and belong to both the families of spectral risk measures and concave distortion risk measures. This paper provides the first detailed study exploring implications of the extremile terminology in a general setting of presence of covariates. We rely on local linear (least squares) check function minimization for estimating conditional extremiles and deriving the asymptotic normality of their estimators. We also extend extremile regression far into the tails of heavy-tailed distributions. Extrapolated estimators are constructed and their asymptotic theory is developed. Some applications to real data are provided.

Suggested Citation

  • Abdelaati Daouia & Irene Gijbels & Gilles Stupfler, 2021. "Extremile regression," Post-Print hal-03181017, HAL.
    • Handle: RePEc:hal:journl:hal-03181017
    DOI: 10.1080/01621459.2021.1875837
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    2. Abdelaati Daouia & Irène Gijbels & Gilles Stupfler, 2019. "Extremiles: A New Perspective on Asymmetric Least Squares," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1366-1381, July.
    3. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.
    4. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    5. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Genest Christian & Scherer Matthias, 2023. "When copulas and smoothing met: An interview with Irène Gijbels," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-16, January.
    2. Chen, Yu & Ma, Mengyuan & Sun, Hongfang, 2023. "Statistical inference for extreme extremile in heavy-tailed heteroscedastic regression model," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 142-162.
    3. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    4. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    5. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stéphane Girard & Gilles Claude Stupfler & Antoine Usseglio-Carleve, 2021. "Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models," Post-Print hal-03306230, HAL.
    2. Chen, Yu & Ma, Mengyuan & Sun, Hongfang, 2023. "Statistical inference for extreme extremile in heavy-tailed heteroscedastic regression model," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 142-162.
    3. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    4. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    5. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Testing Granger Non-Causality in Expectiles," University of East Anglia School of Economics Working Paper Series 2023-02, School of Economics, University of East Anglia, Norwich, UK..
    6. John H. J. Einmahl & Fan Yang & Chen Zhou, 2021. "Testing the Multivariate Regular Variation Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 907-919, October.
    7. Marc Henry & Ismael Mourifié, 2013. "Euclidean Revealed Preferences: Testing The Spatial Voting Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 650-666, June.
    8. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    9. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    10. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    11. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    12. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    13. Nolwenn Roudaut & Anne Vanhems, 2012. "Explaining firms efficiency in the Ivorian manufacturing sector: a robust nonparametric approach," Journal of Productivity Analysis, Springer, vol. 37(2), pages 155-169, April.
    14. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    15. Gardes, Laurent & Girard, Stéphane, 2016. "On the estimation of the functional Weibull tail-coefficient," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 29-45.
    16. Jeffrey Racine, 2015. "Mixed data kernel copulas," Empirical Economics, Springer, vol. 48(1), pages 37-59, February.
    17. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Arfat Ahmad Sofi & Subash Sasidharan & Mohammad Younus Bhat, 2023. "Economic growth and club convergence: Is there a neighbour's effect?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(3), pages 2475-2494, July.
    19. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2020. "Robust nonparametric estimation of the conditional tail dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    20. P. Čížek & S. Sadikoglu, 2018. "Bias-corrected quantile regression estimation of censored regression models," Statistical Papers, Springer, vol. 59(1), pages 215-247, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-03181017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.