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Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model

  • You, Jinhong
  • Chen, Gemai
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    This paper studies the estimation of a varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model [Fan and Huang, Manuscript, University of North Carolina, Chapel Hill, USA, 2002]. We focus on the case where some covariates are measured with additive errors. The usual profile least squares and local polynomial estimations lead to biased estimators of the parametric and nonparametric components, respectively, when measurement errors are ignored. By correcting the attenuation we propose a modified profile least squares estimator for the parametric component and a local polynomial estimator for the nonparametric component. We show that the former is consistent, asymptotically normal and achieves the rate in the law of the iterated logarithm, and the latter achieves the optimal strong convergence rate of the usual nonparametric regression. In addition, a consistent estimator is also developed for the error variance. These results can be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.

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

    Volume (Year): 97 (2006)
    Issue (Month): 2 (February)
    Pages: 324-341

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:324-341
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    1. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
    2. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    3. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    4. Eubank, R. L. & Hart, J. D. & Speckman, Paul, 1990. "Trigonometric series regression estimators with an application to partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 70-83, January.
    5. Stephen J. Iturria & Raymond J. Carroll & David Firth, 1999. "Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 547-561.
    6. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-22, July.
    7. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    8. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    9. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    10. Gao, Jiti, 1995. "The laws of the iterated logarithm of some estimates in partly linear models," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 153-162, November.
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