This paper develops a robust profile estimation method for the parametric and nonparametric components of a single-index model when the errors have a strongly unimodal density with unknown nuisance parameter. We derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single-index parameter estimators. Under a log-Gamma model, the sensitivity to anomalous observations is studied using the empirical influence curve. We also discuss a robust K -fold cross-validation procedure to select the smoothing parameters. A numerical study carried on with errors following a log-Gamma model and for contaminated schemes shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one. A real data set illustrates the use of our proposal.

中文翻译：

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当误差具有未知扰动参数的单峰密度时，单指标模型中的稳健估计

本文针对单指标模型的参数和非参数分量开发了一种鲁棒的剖面估计方法，当误差具有强单峰密度且有害参数未知时。我们推导出链接函数估计器的一致性结果以及单指标参数估计器的一致性和渐近分布结果。在 log-Gamma 模型下，使用经验影响曲线研究对异常观察的敏感性。我们还讨论了一个强大的 K 折交叉验证程序来选择平滑参数。根据对数伽玛模型和污染方案进行的带有误差的数值研究表明，所提出的估计器具有良好的稳健性，以及考虑稳健方法而不是经典方法的优势。