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n-uniformly consistent density estimation in nonparametric regression models

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. 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.
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  7. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Discussion Paper 2006-80, Tilburg University, Center for Economic Research.
  8. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  9. repec:cep:stiecm:/2003/450 is not listed on IDEAS
  10. 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.
  11. Einmahl, J.H.J. & van Keilegom, I., 2008. "Specification tests in nonparametric regression," Other publications TiSEM 2c94c2d8-8305-4fb1-b47f-7, Tilburg University, School of Economics and Management.
  12. 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.
  13. 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.
  14. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
  15. 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.
  16. 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.
  17. Kneip A. & Utikal K. J, 2001. "Inference for Density Families Using Functional Principal Component Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 519-542, June.
  18. 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.
  19. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
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