IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v75y2023i2d10.1007_s10463-022-00847-1.html
   My bibliography  Save this article

Quantitative robustness of instance ranking problems

Author

Listed:
  • Tino Werner

    (Institute for Mathematics, Carl von Ossietzky University Oldenburg)

Abstract

Instance ranking problems intend to recover the ordering of the instances in a data set with applications in scientific, social and financial contexts. In this work, we concentrate on the global robustness of parametric instance ranking problems in terms of the breakdown point which measures the fraction of samples that need to be perturbed in order to let the estimator take unreasonable values. Existing breakdown point notions do not cover ranking problems so far. We propose to define a breakdown of the estimator as a sign-reversal of all components which causes the predicted ranking to be potentially completely inverted; therefore, we call it the order-inversal breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for several different carefully distinguished ranking problems and provide least favorable outlier configurations, characterizations of the order-inversal breakdown point and sharp asymptotic upper bounds. We also compute empirical OIBDPs.

Suggested Citation

  • Tino Werner, 2023. "Quantitative robustness of instance ranking problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 335-368, April.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:2:d:10.1007_s10463-022-00847-1
    DOI: 10.1007/s10463-022-00847-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-022-00847-1
    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/s10463-022-00847-1?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. Leon Yang Chu & Hamid Nazerzadeh & Heng Zhang, 2020. "Position Ranking and Auctions for Online Marketplaces," Management Science, INFORMS, vol. 66(8), pages 3617-3634, August.
    2. Tino Werner, 2022. "Elicitability of Instance and Object Ranking," Decision Analysis, INFORMS, vol. 19(2), pages 123-140, June.
    3. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.
    4. Hema Yoganarasimhan, 2020. "Search Personalization Using Machine Learning," Management Science, INFORMS, vol. 66(3), pages 1045-1070, March.
    5. Hubert, Mia, 1997. "The breakdown value of the L1 estimator in contingency tables," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 419-425, May.
    6. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
    7. Peter Ruckdeschel & Nataliya Horbenko, 2012. "Yet another breakdown point notion: EFSBP," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1025-1047, November.
    8. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
    Full references (including those not matched with items on IDEAS)

    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. repec:hum:wpaper:sfb649dp2006-050 is not listed on IDEAS
    2. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    3. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    4. Cizek, P., 2007. "Efficient Robust Estimation of Time-Series Regression Models," Discussion Paper 2007-95, Tilburg University, Center for Economic Research.
    5. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    6. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    7. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    8. Čίžek, Pavel & Härdle, Wolfgang Karl, 2006. "Robust econometrics," SFB 649 Discussion Papers 2006-050, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Tino Werner, 2022. "Elicitability of Instance and Object Ranking," Decision Analysis, INFORMS, vol. 19(2), pages 123-140, June.
    10. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    11. Batool, Fatima & Hennig, Christian, 2021. "Clustering with the Average Silhouette Width," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    12. Grané, Aurea & Veiga, Helena, 2010. "Outliers in Garch models and the estimation of risk measures," DES - Working Papers. Statistics and Econometrics. WS ws100502, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Carnero, María Ángeles, 2004. "Spurious and hidden volatility," DES - Working Papers. Statistics and Econometrics. WS ws042007, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Omid Rafieian & Hema Yoganarasimhan, 2021. "Targeting and Privacy in Mobile Advertising," Marketing Science, INFORMS, vol. 40(2), pages 193-218, March.
    15. Ana Helena Tavares & Jakob Raymaekers & Peter J. Rousseeuw & Paula Brito & Vera Afreixo, 2020. "Clustering genomic words in human DNA using peaks and trends of distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 57-76, March.
    16. Jussi Tolvi, 2001. "Outliers in eleven Finnish macroeconomic time series," Finnish Economic Papers, Finnish Economic Association, vol. 14(1), pages 14-32, Spring.
    17. Cizek, Pavel, 2008. "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 687-696, June.
    18. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2008. "Estimating and Forecasting GARCH Volatility in the Presence of Outiers," Working Papers. Serie AD 2008-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    19. Cizek, P. & Hardle, W., 2006. "Robust estimation of dimension reduction space," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 545-555, November.
    20. Behmiri, Niaz Bashiri & Manera, Matteo, 2015. "The role of outliers and oil price shocks on volatility of metal prices," Resources Policy, Elsevier, vol. 46(P2), pages 139-150.
    21. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.

    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:aistmt:v:75:y:2023:i:2:d:10.1007_s10463-022-00847-1. 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.