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Asymptotic Normality of a Combined Regression Estimator

  • Fan, Yanqin
  • Ullah, Aman

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.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 71 (1999)
Issue (Month): 2 (November)
Pages: 191-240

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Handle: RePEc:eee:jmvana:v:71:y:1999:i:2:p:191-240
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  1. Lavergne, P. & Vuong, Q., 1992. "Nonparametric Selection of Regressors : the Nonnested Case," Papers 9204, Southern California - Department of Economics.
  2. 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.
  3. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  4. 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.
  5. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. de Jong, Peter, 1990. "A central limit theorem for generalized multilinear forms," Journal of Multivariate Analysis, Elsevier, vol. 34(2), pages 275-289, August.
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