IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/40452.html
   My bibliography  Save this paper

Asymptotic theory for partly linear models

Author

Listed:
  • Gao, Jiti

Abstract

This paper considers a partially linear model of the form y = x beta + g(t) + e, where beta is an unknown parameter vector, g(.) is an unknown function, and e is an error term. Based on a nonparametric estimate of g(.), the parameter beta is estimated by a semiparametric weighted least squares estimator. An asymptotic theory is established for the consistency of the estimators.

Suggested Citation

  • Gao, Jiti, 1994. "Asymptotic theory for partly linear models," MPRA Paper 40452, University Library of Munich, Germany, revised 02 Dec 1994.
    • Handle: RePEc:pra:mprapa:40452
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/40452/1/MPRA_paper_40452.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    2. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    3. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    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. Aneiros-Perez, G. & Vilar-Fernandez, J.M., 2008. "Local polynomial estimation in partial linear regression models under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2757-2777, January.
    2. Q. Shao, 2009. "Seasonality analysis of time series in partial linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 827-837.
    3. You, Jinhong & Zhou, Xian, 2006. "Statistical inference in a panel data semiparametric regression model with serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 844-873, April.
    4. Zhensheng Huang, 2012. "Empirical likelihood for varying-coefficient single-index model with right-censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 55-71, January.
    5. 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.
    6. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    7. Huang, Tzee-Ming & Chen, Hung, 2008. "Estimating the parametric component of nonlinear partial spline model," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1665-1680, September.
    8. Xiaohui Liu & Zhizhong Wang & Xuemei Hu, 2011. "Testing heteroscedasticity in partially linear models with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 321-337.

    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. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. Ai, Chunrong & McFadden, Daniel, 1997. "Estimation of some partially specified nonlinear models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 1-37.
    4. Kourtellos, Andros & Stengos, Thanasis & Sun, Yiguo, 2022. "Endogeneity In Semiparametric Threshold Regression," Econometric Theory, Cambridge University Press, vol. 38(3), pages 562-595, June.
    5. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    6. 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.
    7. Roger D. Peng & Francesca Dominici & Thomas A. Louis, 2006. "Model choice in time series studies of air pollution and mortality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 179-203, March.
    8. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    9. Golubev, Georgi & Härdle, Wolfgang, 1997. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 1997,100, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Häggström, Jenny, 2013. "Bandwidth selection for backfitting estimation of semiparametric additive models: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 136-148.
    11. 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.
    12. Germán Aneiros & Alejandro Quintela, 2001. "Asymptotic properties in partial linear models under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 333-355, December.
    13. Biqing Cai & Jiti Gao, 2017. "A simple nonlinear predictive model for stock returns," Monash Econometrics and Business Statistics Working Papers 18/17, Monash University, Department of Econometrics and Business Statistics.
    14. Biqing Cai & Jiti Gao, 2013. "Hermite Series Estimation in Nonlinear Cointegrating Models," Monash Econometrics and Business Statistics Working Papers 17/13, Monash University, Department of Econometrics and Business Statistics.
    15. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    16. Sung Wan Han & Rickson C. Mesquita & Theresa M. Busch & Mary E. Putt, 2014. "A method for choosing the smoothing parameter in a semi-parametric model for detecting change-points in blood flow," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 26-45, January.
    17. Wang, Xiaoguang & Lu, Dawei & Song, Lixin, 2013. "Statistical inference for partially linear stochastic models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 150-160.
    18. Haotian Chen & Xibin Zhang, 2014. "Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption," Monash Econometrics and Business Statistics Working Papers 28/14, Monash University, Department of Econometrics and Business Statistics.
    19. Yongsong Qin & Jianjun Li, 2011. "Empirical likelihood for partially linear models with missing responses at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 497-511.
    20. repec:hal:journl:peer-00844810 is not listed on IDEAS
    21. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.

    More about this item

    Keywords

    Asymptotic normality; linear process; partly linear model; strong consistency;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:pra:mprapa:40452. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.