论文标题
强大的惩罚条估计和差额罚款
Robust penalized spline estimation with difference penalties
论文作者
论文摘要
通过离散差惩罚（P-Splines）进行惩罚的样条估计是半参数模型的流行估计方法，但是经典的最小二乘估计器对与其理想模型假设的偏差高度敏感。为了解决这种缺陷，引入和研究了基于一般损失功能的广泛的P型估计量。可靠的估计器是通过精心挑选的损失函数（例如Huber或Tukey损失函数）获得的。初步规模估计器也可以包括在损失函数中。结果表明，这类P-Spline估计量具有与最小二乘P-Splines相同的最佳渐近特性，从而为其使用提供了强大的理论动机。提出的估计器可以通过简单地适应良好的迭代最小二乘算法来计算得很有效，并且即使在有限样本中也表现出卓越的性能，这一点通过数值研究和真实数据示例证明。
Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model assumptions. To remedy this deficiency, a broad class of P-spline estimators based on general loss functions is introduced and studied. Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. A preliminary scale estimator can also be included in the loss function. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical motivation for its use. The proposed estimators may be computed very efficiently through a simple adaptation of well-established iterative least squares algorithms and exhibit excellent performance even in finite samples, as evidenced by a numerical study and a real-data example.
