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n-uniformly consistent density estimation in nonparametric regression models

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Author Info

  • Escanciano, Juan Carlos
  • Jacho-Chávez, David T.

Abstract

The paper introduces a n-consistent estimator of the probability density function of the response variable in a nonparametric regression model. The proposed estimator is shown to have a (uniform) asymptotic normal distribution, and it is computationally very simple to calculate. A Monte Carlo experiment confirms our theoretical results. The results derived in the paper adapt general U-processes theory to the inclusion of infinite dimensional nuisance parameters.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304407611001989
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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 2 ()
Pages: 305-316

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Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:305-316

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Density estimation; Kernel smoothing; U-processes;

References

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  1. Michael G. Akritas, 2001. "Non-parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(3), pages 549-567.
  2. 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, 09.
  3. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.
  4. Anton Schick & Wolfgang Wefelmeyer, 2004. "Root "n" consistent and optimal density estimators for moving average processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(1), pages 63-78.
  5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
  6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  7. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  8. Arthur Lewbel, 2000. "Endogenous Selection Or Treatment Model Estimation," Boston College Working Papers in Economics 462, Boston College Department of Economics, revised 13 Jun 2007.
  9. Einmahl, J.H.J. & Keilegom, I. van, 2006. "Tests for Independence in Nonparametric Regression," Discussion Paper 2006-80, Tilburg University, Center for Economic Research.
  10. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  11. Anton Schick & Wolfgang Wefelmeyer, 2002. "Estimating the Innovation Distribution in Nonlinear Autoregressive Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 245-260, June.
  12. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
  13. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
  14. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
  15. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  16. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
  17. Ahn, Hyungtaik, 1997. "Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors," Econometric Theory, Cambridge University Press, vol. 13(01), pages 3-31, February.
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Citations

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Cited by:
  1. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
  2. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2013. "Bayesian bandwidth selection for a nonparametric regession model with mixed types of regressors," Monash Econometrics and Business Statistics Working Papers 13/13, Monash University, Department of Econometrics and Business Statistics.
  3. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.

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