Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low‐rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast and compare favourably against existing methods.

中文翻译：

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通过特征系统截断平滑样条的低秩逼近

平滑样条为非参数估计和推断提供了强大而灵活的方法。由于具有立方时间复杂性，因此将平滑样条曲线模型拟合到大数据在计算上是令人望而却步的。在本文中，我们使用理论上的最佳特征空间来推导平滑样条估计的低秩近似。我们开发了一种在未知的情况下对本征系统进行近似的方法，并为近似估计导出误差范围。所提出的方法易于使用现有软件来实现。大量的仿真表明，新方法准确，快速，并且与现有方法相比具有优势。