IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v64y2002i3p447-466.html
   My bibliography  Save this article

Estimates of regression coefficients based on the sign covariance matrix

Author

Listed:
  • Esa Ollila
  • Hannu Oja
  • Thomas P. Hettmansperger

Abstract

Summary. A new estimator of the regression parameters is introduced in a multivariate multiple‐regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linear in elliptic cases; for the least squares (LS) estimate it is quadratic. The asymptotic relative efficiencies with respect to the LS estimate are given in the multivariate normal as well as the t‐distribution cases. The SCM regression estimate is highly efficient in the multivariate normal case and, for heavy‐tailed distributions, it performs better than the LS estimate. Simulations are used to consider finite sample efficiencies with similar results. The theory is illustrated with an example.

Suggested Citation

  • Esa Ollila & Hannu Oja & Thomas P. Hettmansperger, 2002. "Estimates of regression coefficients based on the sign covariance matrix," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 447-466, August.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:447-466
    DOI: 10.1111/1467-9868.00344
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00344
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00344?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
    ---><---

    References listed on IDEAS

    as
    1. Möttönen, J. & Hettmansperger, T. P. & Oja, H. & Tienari, J., 1998. "On the Efficiency of Affine Invariant Multivariate Rank Tests," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 118-132, July.
    2. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    2. Biau, Gérard & Devroye, Luc & Dujmović, Vida & Krzyżak, Adam, 2012. "An affine invariant k-nearest neighbor regression estimate," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 24-34.
    3. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    4. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    5. Nadar, M. & Hettmansperger, T. P. & Oja, H., 2003. "The asymptotic covariance matrix of the Oja median," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 431-442, October.
    6. Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.
    7. Ella Roelant & Stefan Van Aelst, 2007. "An L1-type estimator of multivariate location and shape," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 381-393, February.
    8. Ollila, Esa & Oja, Hannu & Croux, Christophe, 2003. "The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 328-355, November.
    9. Jung, Kang-Mo, 2005. "Multivariate least-trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 307-316, February.
    10. Ella Roelant & Stefan Aelst, 2007. "An L1-type estimator of multivariate location and shape," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 381-393, February.

    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. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    3. Sakineh Dehghan & Mohammad Reza Faridrohani, 2019. "Affine invariant depth-based tests for the multivariate one-sample location problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 671-693, September.
    4. Ollila, Esa & Oja, Hannu & Croux, Christophe, 2003. "The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 328-355, November.
    5. Furno, Marilena, 1998. "Estimating the variance of the LAD regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 11-26, March.
    6. repec:hal:spmain:info:hdl:2441/3qnaslliat80pbqa8t90240unj is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    8. 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).
    9. Molyneux, Philip & Pancotto, Livia & Reghezza, Alessio & Rodriguez d'Acri, Costanza, 2022. "Interest rate risk and monetary policy normalisation in the euro area," Journal of International Money and Finance, Elsevier, vol. 124(C).
    10. 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.
    11. Georgios Bertsatos & Plutarchos Sakellaris & Mike G. Tsionas, 2022. "Extensions of the Pesaran, Shin and Smith (2001) bounds testing procedure," Empirical Economics, Springer, vol. 62(2), pages 605-634, February.
    12. Salimata Sissoko, 2011. "Working Paper 03-11 - Niveau de décentralisation de la négociation et structure des salaires," Working Papers 1103, Federal Planning Bureau, Belgium.
    13. 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.
    14. 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.
    15. Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October.
    16. Cuesta, Lizeth & Ruiz, Yomara, 2021. "Efecto de la globalización sobre la desigualdad. Un estudio global para 104 países usando regresiones cuantílicas [Effect of globalization on inequality. A global study for 104 countries using quan," MPRA Paper 111022, University Library of Munich, Germany.
    17. Dutta, Anupam & Bouri, Elie & Rothovius, Timo & Uddin, Gazi Salah, 2023. "Climate risk and green investments: New evidence," Energy, Elsevier, vol. 265(C).
    18. 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.
    19. Guili Liao & Qimeng Liu & Rongmao Zhang & Shifang Zhang, 2022. "Rank test of unit‐root hypothesis with AR‐GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 695-719, September.
    20. Shweta Bahl & Ajay Sharma, 2021. "Education–Occupation Mismatch and Dispersion in Returns to Education: Evidence from India," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 251-298, January.
    21. Nguyen, Thao & Bai, Min & Hou, Greg & Vu, Manh-Chien, 2020. "State ownership and adjustment speed toward target leverage: Evidence from a transitional economy," Research in International Business and Finance, Elsevier, vol. 53(C).
    22. Asongu, Simplice A. & Odhiambo, Nicholas M., 2021. "Inequality, finance and renewable energy consumption in Sub-Saharan Africa," Renewable Energy, Elsevier, vol. 165(P1), pages 678-688.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssb:v:64:y:2002:i:3:p:447-466. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.