IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v26y2010i05p1529-1564_99.html
   My bibliography  Save this article

Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model

Author

Listed:
  • Kong, Efang
  • Linton, Oliver
  • Xia, Yingcun

Abstract

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi, Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.

Suggested Citation

  • 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.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:05:p:1529-1564_99
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466609990661/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    2. Linton, Oliver, 2001. "ESTIMATING ADDITIVE NONPARAMETRIC MODELS BY PARTIAL Lq NORM: THE CURSE OF FRACTIONALITY," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1037-1050, December.
    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    4. Hengartner, Nicolas W. & Sperlich, Stefan, 2005. "Rate optimal estimation with the integration method in the presence of many covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 246-272, August.
    5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    6. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    7. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    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, 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.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    3. Sungwon Lee & Joon H. Ro, 2020. "Nonparametric Tests for Conditional Quantile Independence with Duration Outcomes," Working Papers 2013, Research Institute for Market Economy, Sogang University.
    4. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    5. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
    6. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    7. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    8. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    9. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Hidehiko Ichimura & Whitney K. Newey, 2015. "The Influence Function of Semiparametric Estimators," CIRJE F-Series CIRJE-F-985, CIRJE, Faculty of Economics, University of Tokyo.
    11. 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.
    12. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    13. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    14. Jiang, Jiancheng & Jiang, Xuejun & Li, Jingzhi & Liu, Yi & Yan, Wanfeng, 2017. "Spatial quantile estimation of multivariate threshold time series models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 772-781.
    15. Torgovitsky, Alexander, 2017. "Minimum distance from independence estimation of nonseparable instrumental variables models," Journal of Econometrics, Elsevier, vol. 199(1), pages 35-48.
    16. 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.
    17. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    18. Holger Dette & Matthias Guhlich & Natalie Neumeyer, 2015. "Testing for additivity in nonparametric quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 437-477, June.
    19. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    20. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.

    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:cup:etheor:v:26:y:2010:i:05:p:1529-1564_99. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.cambridge.org/ect .

    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: Keith Waters (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.