论文标题
在高维度中发出鲁棒性：复合估计与模型平均估计
Detangling robustness in high dimensions: composite versus model-averaged estimation
论文作者
论文摘要
尽管在实践中无处不在，但在正规化估计和高维度的背景下，鲁棒方法尚未完全理解。即使简单的问题也很快变得具有挑战性。例如，经典统计理论确定了模型平均和复合分位数估计之间的等价性。但是，对于鼓励稀疏性的方法之间的这种等价性，几乎一无所知。本文提供了一个工具箱，以进一步研究这些环境中的鲁棒性，并专注于预测。特别是，我们研究了最佳加权模型平均和复合$ l_1 $ regultarized估计。通过最小化渐近平均平方误差来确定最佳权重。这种方法结合了正则化的效果，而没有理想选择的假设，正如在实践中经常使用的那样。然后，此类权重是预测质量的最佳选择。通过一项广泛的模拟研究，我们表明，没有一种方法系统地表现出其他方法。但是，我们发现即使在高斯模型噪声的情况下，即使是模型平均且复合的分位数估计器通常都优于最小二乘方法。实际数据应用程序通过重建压缩音频信号来证明该方法的实际用途。
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory identifies equivalence between model-averaged and composite quantile estimation. However, little to nothing is known about such equivalence between methods that encourage sparsity. This paper provides a toolbox to further study robustness in these settings and focuses on prediction. In particular, we study optimally weighted model-averaged as well as composite $l_1$-regularized estimation. Optimal weights are determined by minimizing the asymptotic mean squared error. This approach incorporates the effects of regularization, without the assumption of perfect selection, as is often used in practice. Such weights are then optimal for prediction quality. Through an extensive simulation study, we show that no single method systematically outperforms others. We find, however, that model-averaged and composite quantile estimators often outperform least-squares methods, even in the case of Gaussian model noise. Real data application witnesses the method's practical use through the reconstruction of compressed audio signals.
