IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i17-18p1271-1283.html
   My bibliography  Save this article

Sieve least squares estimation for partially nonlinear models

Author

Listed:
  • Song, Lixin
  • Zhao, Yue
  • Wang, Xiaoguang

Abstract

This paper considers a partially nonlinear model , which is a sub-model of the general partially nonlinear model but has some particular advantages in statistical inference. We develop a sieve least squares method to estimate the parameters of the parametric part and the nonparametric part. The consistency and asymptotic normality of the estimator for the parametric part are established. Simulation results show that the sieve estimators perform quite well.

Suggested Citation

  • Song, Lixin & Zhao, Yue & Wang, Xiaoguang, 2010. "Sieve least squares estimation for partially nonlinear models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1271-1283, September.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1271-1283
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00113-6
    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. Xue H. & Lam K.F. & Li G., 2004. "Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 346-356, January.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Liang, Hua, 1995. "Second-order asymptotic efficiency of PMLE in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 273-279, August.
    4. Runze Li & Lei Nie, 2008. "Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications," Biometrics, The International Biometric Society, vol. 64(3), pages 904-911, September.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    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. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    2. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.
    3. Wang, Zhaoliang & Xue, Liugen & Liu, Juanfang, 2019. "Checking nonparametric component for partially nonlinear model with missing response," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 1-8.
    4. Xiaoshuang Zhou & Peixin Zhao & Yujie Gai, 2022. "Imputation-based empirical likelihood inferences for partially nonlinear quantile regression models with missing responses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 705-722, December.

    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. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    2. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    4. Wang, Xiuli & Zhao, Shengli & Wang, Mingqiu, 2017. "Restricted profile estimation for partially linear models with large-dimensional covariates," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 71-76.
    5. Daniel Becker & Alois Kneip & Valentin Patilea, 2021. "Semiparametric inference for partially linear regressions with Box-Cox transformation," Papers 2106.10723, arXiv.org.
    6. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    7. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    8. Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
    9. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    10. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    11. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    12. Robinson, Peter M. & Thawornkaiwong, Supachoke, 2012. "Statistical inference on regression with spatial dependence," Journal of Econometrics, Elsevier, vol. 167(2), pages 521-542.
    13. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    14. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    15. Wang, Zhaoliang & Xue, Liugen & Liu, Juanfang, 2019. "Checking nonparametric component for partially nonlinear model with missing response," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 1-8.
    16. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    17. Gao, Jiti, 2012. "Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models," MPRA Paper 39256, University Library of Munich, Germany, revised 14 May 2012.
    18. 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.
    19. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    20. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.

    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:stapro:v:80:y:2010:i:17-18:p:1271-1283. 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.