Abstract To avoid the effect of distributional misspecification in the model-based regression, we propose an essentially nonparametric symmetric error distribution and construct a so-called doubly smoothed (DS) likelihood function by applying the same amount of smoothing to both the model and given data. To compute the DS maximum likelihood estimator based on the DS likelihood, we propose an approximated DS likelihood which has the form of a semiparametric mixture likelihood and apply some existing algorithms in the nonparametric mixture literature. The consistency of the DS maximum likelihood estimator is also established with any fixed smoothing parameter. Through numerical studies, we demonstrate that the proposed regression coefficient estimator has relatively good performance in terms of efficiency across a wide range of error distributions and robustness against outliers.

中文翻译：

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具有对称误差的线性回归的半参数估计

摘要 为了避免在基于模型的回归中分布错误指定的影响，我们提出了一个基本上非参数的对称误差分布，并通过对模型和给定数据应用相同数量的平滑来构建所谓的双平滑 (DS) 似然函数. 为了基于 DS 似然计算 DS 最大似然估计量，我们提出了一种近似的 DS 似然，它具有半参数混合似然的形式，并应用了非参数混合文献中的一些现有算法。DS 最大似然估计量的一致性也建立在任何固定的平滑参数上。通过数值研究，