IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200256.html
   My bibliography  Save this paper

Semi-parametric estimation of generalized partially linear single-index models

Author

Listed:
  • Xia, Yingcun
  • Härdle, Wolfgang

Abstract

One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations. In this paper, efficient, constructible and practicable estimators of GPLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. (1997): no root-n pilot estimator for the single index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).

Suggested Citation

  • Xia, Yingcun & Härdle, Wolfgang, 2002. "Semi-parametric estimation of generalized partially linear single-index models," SFB 373 Discussion Papers 2002,56, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200256
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/65301/1/726810495.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    2. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    3. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
    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. Tanha, Hassan & Dempsey, Michael, 2015. "The asymmetric response of volatility to market changes and the volatility smile: Evidence from Australian options," Research in International Business and Finance, Elsevier, vol. 34(C), pages 164-176.
    2. Ormos, Mihály & Timotity, Dusan, 2016. "Unravelling the asymmetric volatility puzzle: A novel explanation of volatility through anchoring," Economic Systems, Elsevier, vol. 40(3), pages 345-354.
    3. Horpestad, Jone B. & Lyócsa, Štefan & Molnár, Peter & Olsen, Torbjørn B., 2019. "Asymmetric volatility in equity markets around the world," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 540-554.
    4. Aboura, Sofiane & Wagner, Niklas, 2016. "Extreme asymmetric volatility: Stress and aggregate asset prices," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 47-59.
    5. Michel Delecroix & Marian Hristache & Valentin Patilea, 2004. "On Semiparametric estimation in Single-Index Regression," Working Papers 2004-17, Center for Research in Economics and Statistics.
    6. Bugge, Sebastian A. & Guttormsen, Haakon J. & Molnár, Peter & Ringdal, Martin, 2016. "Implied volatility index for the Norwegian equity market," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 133-141.

    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. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    2. Yingcun Xia & Wolfgang Härdle & Oliver Linton, 2009. "Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator," SFB 649 Discussion Papers SFB649DP2009-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    4. Wang, Qihua & Härdle, Wolfgang & Linton, Oliver, 2002. "Semiparametric regression analysis under imputation for missing response data," SFB 373 Discussion Papers 2002,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    7. McMillen, Daniel P., 2001. "Nonparametric Employment Subcenter Identification," Journal of Urban Economics, Elsevier, vol. 50(3), pages 448-473, November.
    8. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series 493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    10. Chen, Songxi, 2012. "Estimation in semiparametric models with missing data," MPRA Paper 46216, University Library of Munich, Germany.
    11. Ouyang, Yusi & Pinstrup-Andersen, Per, 2012. "Health Inequality between Ethnic Minority and Han Populations in China," World Development, Elsevier, vol. 40(7), pages 1452-1468.
    12. Lewbel, Arthur & Lin, Xirong, 2022. "Identification of semiparametric model coefficients, with an application to collective households," Journal of Econometrics, Elsevier, vol. 226(2), pages 205-223.
    13. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    14. Fernández Sainz, Ana Isabel & Rodríguez Poo, Juan M. & Villanúa Martín, Inmaculada, 1999. "Finite sample behavior of two step estimators in selection models," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    15. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    16. Atak, Alev & Linton, Oliver & Xiao, Zhijie, 2011. "A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom," Journal of Econometrics, Elsevier, vol. 164(1), pages 92-115, September.
    17. Song Chen & Ingrid Van Keilegom, 2013. "Estimation in semiparametric models with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 785-805, August.
    18. Ana Fernandez Sainz & Juan Rodriguez-Poo & Inmaculada Villanua Martin, 2002. "Finite sample behavior of two step estimators in selection models," Computational Statistics, Springer, vol. 17(1), pages 1-16, March.
    19. Stoker, Thomas M., 1996. "Smoothing bias in the measurement of marginal effects," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 49-84.
    20. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000.

    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:zbw:sfb373:200256. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.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.