IDEAS home Printed from https://ideas.repec.org/p/azt/cemmap/46-14.html
   My bibliography  Save this paper

Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions

Author

Listed:
  • Xiaohong Chen
  • Timothy M. Christensen

Abstract

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n= log n)–p=(2p+d) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 + (d=p))th absolute moment for d=p

Suggested Citation

  • Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," CeMMAP working papers 46/14, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:46/14
    DOI: 10.1920/wp.cem.2014.4614
    as

    Download full text from publisher

    File URL: https://www.cemmap.ac.uk/wp-content/uploads/2020/08/CWP4614.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.1920/wp.cem.2014.4614?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
    ---><---

    References listed on IDEAS

    as
    1. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression," Cowles Foundation Discussion Papers 1923, Cowles Foundation for Research in Economics, Yale University.
    2. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1433-1445, October.
    3. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
    4. Song, Kyungchul, 2008. "Uniform Convergence Of Series Estimators Over Function Spaces," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1463-1499, December.
    5. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    6. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    7. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    8. 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.
    9. Jungyoon Lee & Peter M Robinson, 2013. "Series Estimation under Cross-sectional Dependence," STICERD - Econometrics Paper Series 570, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    11. 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.
    12. P. M. Robinson, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 511-534.
    13. repec:cep:stiecm:/2013/570 is not listed on IDEAS
    14. Huang, Jianhua Z., 2003. "Asymptotics for polynomial spline regression under weak conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 207-216, November.
    15. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    16. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    17. Qi Li & Jeffrey Scott Racine, 2006. "Density Estimation, from Nonparametric Econometrics: Theory and Practice," Introductory Chapters, in: Nonparametric Econometrics: Theory and Practice, Princeton University Press.
    18. de Jong, Robert M., 2002. "A note on "Convergence rates and asymptotic normality for series estimators": uniform convergence rates," Journal of Econometrics, Elsevier, vol. 111(1), pages 1-9, November.
    19. Lee, Jungyoon & Robinson, Peter M., 2013. "Series estimation under cross-sectional dependence," LSE Research Online Documents on Economics 58188, London School of Economics and Political Science, LSE Library.
    20. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    21. 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.
    22. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
    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. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    2. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression," Cowles Foundation Discussion Papers 1923, Cowles Foundation for Research in Economics, Yale University.
    3. Xiaohong Chen & Timothy M. Christensen, 2013. "Optimal uniform convergence rates for sieve nonparametric instrumental variables regression," CeMMAP working papers 56/13, Institute for Fiscal Studies.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    5. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    6. Byunghoon Kang, 2018. "Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms," Working Papers 240829404, Lancaster University Management School, Economics Department.
    7. Li, Jia & Liao, Zhipeng, 2020. "Uniform nonparametric inference for time series," Journal of Econometrics, Elsevier, vol. 219(1), pages 38-51.
    8. Chen, Xiaohong & Liao, Zhipeng, 2015. "Sieve semiparametric two-step GMM under weak dependence," Journal of Econometrics, Elsevier, vol. 189(1), pages 163-186.
    9. Byunghoon Kang, 2019. "Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms," Papers 1909.12162, arXiv.org, revised Feb 2020.
    10. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "On the asymptotic theory for least squares series: pointwise and uniform results," CeMMAP working papers CWP73/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. 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.
    12. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson, 2021. "Performance of Empirical Risk Minimization for Linear Regression with Dependent Data," Papers 2104.12127, arXiv.org, revised May 2023.
    13. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    14. 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.
    15. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    16. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    17. Xiaohong Chen & Zhipeng Liao & Yixiao Sun, 2012. "Sieve Inference on Semi-nonparametric Time Series Models," Cowles Foundation Discussion Papers 1849, Cowles Foundation for Research in Economics, Yale University.
    18. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    19. 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.
    20. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.

    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:azt:cemmap:46/14. 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: Dermot Watson (email available below). General contact details of provider: https://edirc.repec.org/data/ifsssuk.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.