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

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  • Jan G. De Gooijer
  • Hugo Reichardt

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

  • Jan G. De Gooijer & Hugo Reichardt, 2021. "A multi-step kernel–based regression estimator that adapts to error distributions of unknown form," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 6211-6230, November.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:24:p:6211-6230
    DOI: 10.1080/03610926.2020.1741625
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