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n-uniformly consistent density estimation in nonparametric regression models

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  • 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.

Suggested Citation

  • Escanciano, Juan Carlos & Jacho-Chávez, David T., 2012. "n-uniformly consistent density estimation in nonparametric regression models," Journal of Econometrics, Elsevier, vol. 167(2), pages 305-316.
    • Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:305-316
    DOI: 10.1016/j.jeconom.2011.09.017
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    3. 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.
    4. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(2), pages 277-301, April.
    5. Zapata, Samuel D. & Carpio, Carlos E., 2014. "Distribution-free Methods for Estimation of Willingness to Pay Models Using Discrete Response Valuation Data," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170453, Agricultural and Applied Economics Association.
    6. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    7. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    8. Shang, Han Lin, 2016. "A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 95-104.
    9. Li, Shuo & Tu, Yundong, 2016. "n-consistent density estimation in semiparametric regression models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 91-109.
    10. Henderson Daniel J. & Parmeter Christopher F., 2017. "Root-n Consistent Kernel Density Estimation in Practice," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-10, January.

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