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n-consistent density estimation in semiparametric regression models

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  • Li, Shuo
  • Tu, Yundong

Abstract

The authors propose an estimator for the density of the response variable in the parametric mean regression model where the error density is left unspecified. With the application of empirical process theory, they derive its n-consistency and asymptotical normality. This result is further extended to models which allow possible parametric misspecification on the regression function and a special location–scale model. However, it is found that n-consistency breaks down in the presence of endogeneity. Monte Carlo simulations show that the proposed estimators have superior performance in finite sample compared to other density estimators available in the literature. Two real data illustrations reveal the advantage of the proposed density estimator over the Rosenblatt–Parzen kernel density estimator.

Suggested Citation

  • Li, Shuo & Tu, Yundong, 2016. "n-consistent density estimation in semiparametric regression models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 91-109.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:91-109
    DOI: 10.1016/j.csda.2016.06.013
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    References listed on IDEAS

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    1. Zhao, Zhibiao, 2010. "Density estimation for nonlinear parametric models with conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 155(1), pages 71-82, March.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    4. 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.
    5. 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.
    6. Carlos Martins-Filho & Santosh Mishra & Aman Ullah, 2008. "A Class of Improved Parametrically Guided Nonparametric Regression Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 542-573.
    7. A. Sen & B. Sen, 2014. "Testing independence and goodness-of-fit in linear models," Biometrika, Biometrika Trust, vol. 101(4), pages 927-942.
    8. 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.
    9. Griffin, Peter & Ganderton, Philip T., 1996. "Evidence on omitted variable bias in earnings equations," Economics of Education Review, Elsevier, vol. 15(2), pages 139-148, April.
    10. John DiNardo & Justin L. Tobias, 2001. "Nonparametric Density and Regression Estimation," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 11-28, Fall.
    11. Gan, Li & Zhang, Qinghua, 2006. "The thick market effect on local unemployment rate fluctuations," Journal of Econometrics, Elsevier, vol. 133(1), pages 127-152, July.
    12. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    13. 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, March.
    14. Yin Liao & John Stachurski, 2015. "Simulation-Based Density Estimation for Time Series Using Covariate Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 595-606, October.
    15. 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.
    16. Murtazashvili, Irina & Vozlyublennaia, Nadia, 2012. "The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1057-1066.
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