IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v21y2003i2-2003p109-138n2.html
   My bibliography  Save this article

On the construction of efficient estimators in semiparametric models

Author

Listed:
  • Forrester Jeffrey S.
  • Hooper William J.
  • Peng Hanxiang
  • Schick Anton

Abstract

This paper deals with the construction of efficient estimators in semiparametric models without the sample splitting technique. Schick (1987) gave sufficient conditions using the leave-one-out technique for a construction without sample splitting. His conditions are stronger and more cumbersome to verify than the necessary and sufficient conditions for the existence of efficient estimators which suffice for the construction based on sample splitting. In this paper we use a conditioning argument to weaken Schick′s conditions. We shall then show that in a large class of semiparametric models and for properly chosen estimators of the score function the resulting weaker conditions reduce to the minimal conditions for the construction with sample splitting. In other words, in these models efficient estimators can be constructed without sample splitting under the same conditions as those used for the construction with sample splitting. We demonstrate our results by constructing an efficient estimator using these ideas in a semiparametric additive regression model.

Suggested Citation

  • Forrester Jeffrey S. & Hooper William J. & Peng Hanxiang & Schick Anton, 2003. "On the construction of efficient estimators in semiparametric models," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 109-138, February.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:2/2003:p:109-138:n:2
    DOI: 10.1524/stnd.21.2.109.19007
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/stnd.21.2.109.19007
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1524/stnd.21.2.109.19007?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Schick, Anton, 1996. "Efficient estimation in a semiparametric additive regression model with autoregressive errors," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 339-361, February.
    2. Schick, Anton, 1996. "Root-n-consistent and efficient estimation in semiparametric additive regression models," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 45-51, September.
    3. Anton Schick, 1998. "An Adaptive Estimator of the Autocorrelation Coefficient in Regression Models with Autoregressive Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 575-589, September.
    4. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    5. Schick, Anton, 1999. "Efficient estimation of a shift in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 287-301, February.
    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. Wang, Xueqin & Peng, Hanxiang, 2008. "Moment estimation in a semiparametric generalized linear model," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1624-1633, September.
    2. Wu, Jingjing & Karunamuni, Rohana & Zhang, Biao, 2010. "Minimum Hellinger distance estimation in a two-sample semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1102-1122, May.
    3. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.

    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. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.
    2. Syed Ejaz Ahmed & Ersin Yilmaz & Dursun Aydın, 2025. "Kernel Ridge-Type Shrinkage Estimators in Partially Linear Regression Models with Correlated Errors," Mathematics, MDPI, vol. 13(12), pages 1-33, June.
    3. Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
    4. 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.
    5. Chen, Qitong & Hong, Yongmiao & Li, Haiqi, 2024. "Time-varying forecast combination for factor-augmented regressions with smooth structural changes," Journal of Econometrics, Elsevier, vol. 240(1).
    6. Xinghui Wang & Wenjing Geng & Ruidong Han & Qifa Xu, 2023. "Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-23, March.
    7. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.
    8. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    9. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    10. WenWu Wang & Ping Yu, 2023. "Nonequivalence of two least-absolute-deviation estimators for mediation effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 370-387, March.
    11. Min Ren & Shengli Zhao & Mingqiu Wang & Xinbei Zhu, 2024. "Robust optimal subsampling based on weighted asymmetric least squares," Statistical Papers, Springer, vol. 65(4), pages 2221-2251, June.
    12. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    13. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    14. Wolff Rodney & Yao Qiwei & Tong Howell, 2004. "Statistical Tests for Lyapunov Exponents of Deterministic Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-19, May.
    15. Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2011. "Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis," Working Papers ECARES ECARES 2011-038, ULB -- Universite Libre de Bruxelles.
    16. Moreno, Marta & Romo, Juan, 1997. "Bootstrap tests for unit roots based on lad estimation," DES - Working Papers. Statistics and Econometrics. WS 6210, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    18. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    19. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    20. Richard A. Davis & William T. M. Dunsmuir, 1997. "Least Absolute Deviation Estimation for Regression with ARMA Errors," Journal of Theoretical Probability, Springer, vol. 10(2), pages 481-497, April.

    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:bpj:strimo:v:21:y:2003:i:2/2003:p:109-138:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.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.