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A multi-step kernel–based regression estimator that adapts to error distributions of unknown form

Author

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  • De Gooijer, Jan G.
  • Reichardt, Hugo

Abstract

For linear regression models, we propose and study a multi-step kernel density-based estimator that is adaptive to unknown error distributions. We establish asymptotic normality and almost sure convergence. An efficient EM algorithm is provided to implement the proposed estimator. We also compare its finite sample performance with five other adaptive estimators in an extensive Monte Carlo study of eight error distributions. Our method generally attains high mean-square-error efficiency. An empirical example illustrates the gain in efficiency of the new adaptive method when making statistical inference about the slope parameters in three linear regressions.

Suggested Citation

  • De Gooijer, Jan G. & Reichardt, Hugo, 2021. "A multi-step kernel–based regression estimator that adapts to error distributions of unknown form," LSE Research Online Documents on Economics 115083, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:115083
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    File URL: http://eprints.lse.ac.uk/115083/
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    References listed on IDEAS

    as
    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Linton, Oliver & Xiao, Zhijie, 2007. "A Nonparametric Regression Estimator That Adapts To Error Distribution Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(3), pages 371-413, June.
    3. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja, 2017. "Report Cards: The Impact of Providing School and Child Test Scores on Educational Markets," American Economic Review, American Economic Association, vol. 107(6), pages 1535-1563, June.
    4. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    5. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    6. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    7. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    8. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    adaptive estimation; EM algorithm; kernel density estimate; least squares estimate; linear regression;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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