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

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

Abstract

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Y_i,?X_i ) } . 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 functional where some control over higher order terms are required. We apply our results to the estimation of an additive M-regression model.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 05 (October)
Pages: 1529-1564

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

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  1. Sokbae Lee & Joel L. Horowitz, 2004. "Nonparametric Estimation of an Additive Quantile Regression Model," Econometric Society 2004 Far Eastern Meetings 721, Econometric Society.
  2. S. Sperlich & O. Linton & Wolfgang HÄRDLE, 1997. "A Simulation Comparison between Integration and Backfitting Methods of Estimating Separable Nonparametric Regression Models," SFB 373 Discussion Papers 1997,66, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
  4. repec:wop:humbsf:1995-29 is not listed on IDEAS
  5. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  6. Liang Peng & Qiwei Yao, 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.
  7. 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.
  8. Linton, Oliver, 2001. "ESTIMATING ADDITIVE NONPARAMETRIC MODELS BY PARTIAL Lq NORM: THE CURSE OF FRACTIONALITY," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1037-1050, December.
  9. repec:wop:humbsf:1997-66 is not listed on IDEAS
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Cited by:
  1. Wolfgang Karl Härdle & Ya’acov Ritov & Song Song, 2010. "Partial Linear Quantile Regression and Bootstrap Confidence Bands," SFB 649 Discussion Papers SFB649DP2010-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2013. "Estimating the Impact of Means-tested Subsidies under Treatment Externalities with Application to Anti-Malarial Bednets," CREATES Research Papers 2013-06, School of Economics and Management, University of Aarhus.
  3. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2009. "Intersection Bounds: estimation and inference," CeMMAP working papers CWP19/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Marc Hallin & Zudi Lu & Davy Paindaveine & Miroslav Siman, 2012. "Local Constant and Local Bilinear Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2012-003, ULB -- Universite Libre de Bruxelles.
  5. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val, 2011. "Conditional quantile processes based on series or many regressors," CeMMAP working papers CWP19/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2011. "Semiparametric Estimation with Generated Covariates," IZA Discussion Papers 6084, Institute for the Study of Labor (IZA).
  7. Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
  8. Rothe, Christoph & Firpo, Sergio, 2013. "Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions," IZA Discussion Papers 7564, Institute for the Study of Labor (IZA).
  9. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(05), pages 941-968, October.
  10. Wolfgang Karl Härdle & Ya'acov Ritov & Weining Wang, 2013. "Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators," SFB 649 Discussion Papers SFB649DP2013-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Härdle, 2014. "Confidence Corridors for Multivariate Generalized Quantile Regression," SFB 649 Discussion Papers SFB649DP2014-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. 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.

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