IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v70y2008i2p389-412.html
   My bibliography  Save this article

Semiparametrically efficient inference based on signs and ranks for median‐restricted models

Author

Listed:
  • Marc Hallin
  • Catherine Vermandele
  • Bas J. M. Werker

Abstract

Summary. Since the pioneering work of Koenker and Bassett, median‐restricted models have attracted considerable interest. Attention in these models, so far, has focused on least absolute deviation (auto‐)regression quantile estimation and the corresponding sign tests. These methods use a pseudolikelihood that is based on a double‐exponential reference density and enjoy quite attractive properties of root n consistency (for estimators) and distribution freeness (for tests). The paper extends these results to general, i.e. not necessarily double‐exponential, reference densities. Using residual signs and ranks (not signed ranks) and a general reference density f, we construct estimators that remain root n consistent, irrespective of the true underlying density g (i.e. also for g /=f). However, instead of reaching semiparametric efficiency bounds under double‐exponential g, they reach these bounds when g coincides with the chosen reference density f. Moreover, we show that choosing reference densities other than the double‐exponential in applications can lead to sizable gains in efficiency. The particular case of median regression is treated in detail; extensions to general quantile regression, heteroscedastic errors and time series models are briefly described. The performance of the method is also assessed by simulation and illustrated on financial data.

Suggested Citation

  • Marc Hallin & Catherine Vermandele & Bas J. M. Werker, 2008. "Semiparametrically efficient inference based on signs and ranks for median‐restricted models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 389-412, April.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:389-412
    DOI: 10.1111/j.1467-9868.2007.00641.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2007.00641.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2007.00641.x?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    2. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    3. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    4. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    5. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    6. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Other publications TiSEM 620d09ba-f476-426d-b236-3, Tilburg University, School of Economics and Management.
    7. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April.
    10. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
    11. Komunjer, Ivana & Vuong, Quang, 2006. "Efficientt Conditional Quantile Estimation: The Time Series Case," University of California at San Diego, Economics Working Paper Series qt78842570, Department of Economics, UC San Diego.
    12. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
    13. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, 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. W. D. Walls & Jordi McKenzie, 2020. "Black swan models for the entertainment industry with an application to the movie business," Empirical Economics, Springer, vol. 59(6), pages 3019-3032, December.
    2. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
    3. Chen, Min & Zhu, Ke, 2014. "Sign-based specification tests for martingale difference with conditional heteroscedasity," MPRA Paper 56347, University Library of Munich, Germany.

    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. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    2. Werker, Bas J M & Andreou, Elena, 2013. "Residual-based Rank Specification Tests for AR-GARCH type models," CEPR Discussion Papers 9583, C.E.P.R. Discussion Papers.
    3. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    4. Elena Andreou & Bas J.M. Werker, 2014. "Residual-based Rank Specification Tests for AR-GARCH type models," University of Cyprus Working Papers in Economics 02-2014, University of Cyprus Department of Economics.
    5. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    6. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    7. Marc Hallin & Abdeslam Serroukh, 1998. "Adaptive Estimation of the Lag of a Long–memory Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 111-129, May.
    8. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.
    9. Andreou, E. & Werker, B.J.M., 2003. "A Simple Asymptotic Analysis of Residual-Based Statistics," Other publications TiSEM 9fe68e51-a026-4660-b6e7-8, Tilburg University, School of Economics and Management.
    10. M. Hallin & D. La Vecchia & H. Liu, 2022. "Center-Outward R-Estimation for Semiparametric VARMA Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 925-938, April.
    11. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Other publications TiSEM 93fe16c1-9f21-4dab-9b73-4, Tilburg University, School of Economics and Management.
    12. Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
    13. Francq, Christian & Zakoian, Jean-Michel, 2023. "Local Asymptotic Normality Of General Conditionally Heteroskedastic And Score-Driven Time-Series Models," Econometric Theory, Cambridge University Press, vol. 39(5), pages 1067-1092, October.
    14. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    15. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Other publications TiSEM bc68a2f2-3ca3-443c-b3ac-f, Tilburg University, School of Economics and Management.
    16. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    17. Douglas Hodgson, 2002. "Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form," Cahiers de recherche CREFE / CREFE Working Papers 146, CREFE, Université du Québec à Montréal.
    18. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2022. "Characterizing M-estimators," Papers 2208.08108, arXiv.org.
    19. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.
    20. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:70:y:2008:i:2:p:389-412. 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.