IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i3d10.1007_s00362-019-01129-4.html
   My bibliography  Save this article

Robustness of the deepest projection regression functional

Author

Listed:
  • Yijun Zuo

    (Michigan State University)

Abstract

Depth notions in regression have been systematically proposed and examined in Zuo ( arXiv:1805.02046 , 2018). One of the prominent advantages of the notion of depth is that it can be directly utilized to introduce median-type deepest estimating functionals (or estimators in the case of empirical distributions) for location or regression parameters in a multi-dimensional setting. Regression depth shares the advantage. Depth induced deepest estimating functionals are expected to inherit desirable and inherent robustness properties (e.g. bounded maximum bias and influence function and high breakdown point) as their univariate location counterpart does. Investigating and verifying the robustness of the deepest projection estimating functional (in terms of maximum bias, asymptotic and finite sample breakdown point, and influence function) is the major goal of this article. It turns out that the deepest projection estimating functional possesses a bounded influence function and the best possible asymptotic breakdown point as well as the best finite sample breakdown point with robust choice of its univariate regression and scale component.

Suggested Citation

  • Yijun Zuo, 2021. "Robustness of the deepest projection regression functional," Statistical Papers, Springer, vol. 62(3), pages 1167-1193, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01129-4
    DOI: 10.1007/s00362-019-01129-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-019-01129-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-019-01129-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Van Aelst, Stefan & Rousseeuw, Peter J., 2000. "Robustness of Deepest Regression," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 82-106, April.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Mingxin Wu & Yijun Zuo, 2008. "Trimmed and winsorized standard deviations based on a scaled deviation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 319-335.
    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. Zuo, Yijun, 2024. "Non-asymptotic robustness analysis of regression depth median," Journal of Multivariate Analysis, Elsevier, vol. 199(C).

    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. Zuo, Yijun, 2021. "Computation of projection regression depth and its induced median," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    2. Yijun Zuo, 2020. "Depth Induced Regression Medians and Uniqueness," Stats, MDPI, vol. 3(2), pages 1-13, April.
    3. Debruyne, M. & Hubert, M. & Portnoy, S. & Vanden Branden, K., 2008. "Censored depth quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1604-1614, January.
    4. Akosah, Nana Kwame & Alagidede, Imhotep Paul & Schaling, Eric, 2020. "Testing for asymmetry in monetary policy rule for small-open developing economies: Multiscale Bayesian quantile evidence from Ghana," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    5. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    6. Salimata Sissoko, 2011. "Working Paper 03-11 - Niveau de décentralisation de la négociation et structure des salaires," Working Papers 1103, Federal Planning Bureau, Belgium.
    7. Korom, Philipp, 2016. "Inherited advantage: The importance of inheritance for private wealth accumulation in Europe," MPIfG Discussion Paper 16/11, Max Planck Institute for the Study of Societies.
    8. Daniele, Vittorio, 2007. "Criminalità e investimenti esteri. Un’analisi per le province italiane [The effect of organized crime on Foreign Investments. An Empirical Analysis for the Italian Provinces]," MPRA Paper 6417, University Library of Munich, Germany.
    9. Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October.
    10. Dutta, Anupam & Bouri, Elie & Rothovius, Timo & Uddin, Gazi Salah, 2023. "Climate risk and green investments: New evidence," Energy, Elsevier, vol. 265(C).
    11. Cowling, Marc & Ughetto, Elisa & Lee, Neil, 2018. "The innovation debt penalty: Cost of debt, loan default, and the effects of a public loan guarantee on high-tech firms," Technological Forecasting and Social Change, Elsevier, vol. 127(C), pages 166-176.
    12. Niematallah Elamin & Mototsugu Fukushige, 2016. "A Quantile Regression Model for Electricity Peak Demand Forecasting: An Approach to Avoiding Power Blackouts," Discussion Papers in Economics and Business 16-22, Osaka University, Graduate School of Economics.
    13. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    14. Jan Fałkowski & Maciej Jakubowski & Paweł Strawiński, 2014. "Returns from income strategies in rural Poland," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 22(1), pages 139-178, January.
    15. Elena Bárcena-Mart�n & Santiago Budr�a & Ana I. Moro-Egido, 2012. "Skill mismatches and wages among European university graduates," Applied Economics Letters, Taylor & Francis Journals, vol. 19(15), pages 1471-1475, October.
    16. Trojanek, Radoslaw & Huderek-Glapska, Sonia, 2018. "Measuring the noise cost of aviation – The association between the Limited Use Area around Warsaw Chopin Airport and property values," Journal of Air Transport Management, Elsevier, vol. 67(C), pages 103-114.
    17. Charlier, Isabelle & Paindaveine, Davy & Saracco, Jérôme, 2015. "Conditional quantile estimation based on optimal quantization: From theory to practice," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 20-39.
    18. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    19. Ron Diris, 2017. "Don't Hold Back? The Effect of Grade Retention on Student Achievement," Education Finance and Policy, MIT Press, vol. 12(3), pages 312-341, Summer.
    20. Huong Thu Le & Ha Trong Nguyen, 2018. "The evolution of the gender test score gap through seventh grade: new insights from Australia using unconditional quantile regression and decomposition," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 7(1), pages 1-42, December.

    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:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01129-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.