IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i5p1162-1184.html
   My bibliography  Save this article

Semi-parametric estimation of partially linear single-index models

Author

Listed:
  • Xia, Yingcun
  • Härdle, Wolfgang

Abstract

One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) 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 PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477-489]: 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, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:5:p:1162-1184
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00199-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. 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.
    4. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    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.
    6. 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.
    7. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    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. 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.
    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. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    4. 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.
    5. 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.
    6. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    7. 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.
    8. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    9. 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.
    10. Song Song, 2011. "Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approach," Papers 1106.3921, arXiv.org, revised Jun 2011.
    11. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    12. McMillen, Daniel P., 2001. "Nonparametric Employment Subcenter Identification," Journal of Urban Economics, Elsevier, vol. 50(3), pages 448-473, November.
    13. 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.
    14. 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.
    15. Chen, Songxi, 2012. "Estimation in semiparametric models with missing data," MPRA Paper 46216, University Library of Munich, Germany.
    16. 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.
    17. 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.
    18. 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).
    19. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.
    20. 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.

    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:eee:jmvana:v:97:y:2006:i:5:p:1162-1184. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.