IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2112.08546.html
   My bibliography  Save this paper

Uniform Convergence Results for the Local Linear Regression Estimation of the Conditional Distribution

Author

Listed:
  • Haitian Xie

Abstract

This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both $x$ and $y$ and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. We demonstrate the usefulness of these uniform results with two examples: the stochastic equicontinuity condition in $y$, and the estimation of the integrated conditional distribution function.

Suggested Citation

  • Haitian Xie, 2021. "Uniform Convergence Results for the Local Linear Regression Estimation of the Conditional Distribution," Papers 2112.08546, arXiv.org, revised Jun 2023.
  • Handle: RePEc:arx:papers:2112.08546
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2112.08546
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Srinjoy Das & Dimitris N. Politis, 2020. "Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points," The American Statistician, Taylor & Francis Journals, vol. 74(3), pages 233-242, July.
    2. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    3. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    4. Yangin Fan & Emmanuel Guerre, 2016. "Multivariate Local Polynomial Estimators: Uniform Boundary Properties and Asymptotic Linear Representation," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 489-537, Emerald Group Publishing Limited.
    5. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    6. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haitian Xie, 2022. "Nonlinear and Nonseparable Structural Functions in Fuzzy Regression Discontinuity Designs," Papers 2204.08168, arXiv.org, revised Jul 2022.

    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. Juan Carlos Escanciano, 2020. "Uniform Rates for Kernel Estimators of Weakly Dependent Data," Papers 2005.09951, arXiv.org.
    2. Rothe, Christoph & Firpo, Sergio, 2013. "Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions," IZA Discussion Papers 7564, Institute of Labor Economics (IZA).
    3. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    4. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    5. Chiang, Harold D. & Hsu, Yu-Chin & Sasaki, Yuya, 2019. "Robust uniform inference for quantile treatment effects in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 211(2), pages 589-618.
    6. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 819-838, August.
    8. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    9. 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.
    10. Debopam Bhattacharya & Shin Kanaya & Margaret Stevens, 2017. "Are University Admissions Academically Fair?," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 449-464, July.
    11. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    12. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(5), pages 911-952, October.
    13. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    14. Gao, Yichen & Li, Cong & Liang, Zhongwen, 2015. "Binary response correlated random coefficient panel data models," Journal of Econometrics, Elsevier, vol. 188(2), pages 421-434.
    15. Michael Vogt & Oliver Linton, 2015. "Classification of nonparametric regression functions in heterogeneous panels," CeMMAP working papers CWP06/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2013. "Estimating the Impact of Means-tested Subsidies under Treatment Externalities with Application to Anti-Malarial Bednets," Economics Series Working Papers 646, University of Oxford, Department of Economics.
    17. Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(5), pages 935-958, October.
    18. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    19. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    20. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2112.08546. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.