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Asymptotic Normality of a Combined Regression Estimator

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  • Fan, Yanqin
  • Ullah, Aman

Abstract

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.

Suggested Citation

  • Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
  • Handle: RePEc:eee:jmvana:v:71:y:1999:i:2:p:191-240
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    References listed on IDEAS

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    1. Ullah, A. & Vinod, H.D., 1992. ""General Nonparametric Regression Estimation and Testing in Econometrics"," The A. Gary Anderson Graduate School of Management 92-34, The A. Gary Anderson Graduate School of Management. University of California Riverside.
    2. Lavergne, Pascal & Vuong, Quang H, 1996. "Nonparametric Selection of Regressors: The Nonnested Case," Econometrica, Econometric Society, vol. 64(1), pages 207-219, January.
    3. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
    4. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    5. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    6. de Jong, Peter, 1990. "A central limit theorem for generalized multilinear forms," Journal of Multivariate Analysis, Elsevier, vol. 34(2), pages 275-289, August.
    7. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Citations

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    Cited by:

    1. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, Open Access Journal, vol. 1(2), pages 1-23, September.
    2. Maza, Adolfo & Villaverde, Jose, 2004. "Interregional Migration in Spain: A Semiparametric Analysis," The Review of Regional Studies, Southern Regional Science Association, vol. 34(2), pages 156-171.
    3. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    4. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    5. Majda Talamakrouni & Anouar El Ghouch & Ingrid Van Keilegom, 2015. "Guided Censored Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 214-233, March.
    6. El Ghouch, Anouar & Genton, Marc G., 2009. "Local Polynomial Quantile Regression With Parametric Features," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1416-1429.
    7. Chambers, Dustin, 2007. "Trading places: Does past growth impact inequality?," Journal of Development Economics, Elsevier, vol. 82(1), pages 257-266, January.
    8. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.
    9. Adolfo Maza, 2006. "Wage flexibility and the EMU: a nonparametric and semiparametric analysis for the Spanish case," Applied Economics Letters, Taylor & Francis Journals, vol. 13(11), pages 733-736.
    10. Xiangdong Long & Liangjun Su & Aman Ullah, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 109-125, January.
    11. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    12. Wu, Wenjie, 2012. "Spatial variations in amenity values: new evidence from Beijing, China," LSE Research Online Documents on Economics 58536, London School of Economics and Political Science, LSE Library.
    13. Clemente Hernandez-Rodriguez, 2005. "Is the market concentration and interest-rates relationship in the Mexican commercial banking industry a sign of efficiency?," EconoQuantum, Revista de Economia y Negocios, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 1(2), pages 7-38, Enero - J.
    14. Iglesias, Emma M. & Linton, Oliver, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," UC3M Working papers. Economics we094726, Universidad Carlos III de Madrid. Departamento de Economía.
    15. Dustin Chambers, 2005. "Inequality and Growth: A Semiparametric Investigation," Computing in Economics and Finance 2005 132, Society for Computational Economics.
    16. Chambers, Dustin & Wu, Ying & Yao, Hong, 2008. "The impact of past growth on poverty in Chinese provinces," Journal of Asian Economics, Elsevier, vol. 19(4), pages 348-357, August.
    17. Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.

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