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Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model

  • Efang Kong
  • Oliver Linton
  • Yingcun Xia

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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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2009/535.

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Date of creation: Jan 2009
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Handle: RePEc:cep:stiecm:/2009/535
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. 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.
  2. Oliver Linton, 2001. "Estimating additive nonparametric models by partial Lq norm: the curse of fractionality," LSE Research Online Documents on Economics 319, London School of Economics and Political Science, LSE Library.
  3. 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.
  4. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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. 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.
  7. 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.
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