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

Jan G. De Gooijer and Hugo Reichardt

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 24, 6211-6230

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.

Date: 2021
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DOI: 10.1080/03610926.2020.1741625

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