Benkeser David, van der Laan Mark
Proc Int Conf Data Sci Adv Anal. 2016;2016:689-696. doi: 10.1109/DSAA.2016.93. Epub 2016 Dec 26.
Estimation of a regression functions is a common goal of statistical learning. We propose a novel nonparametric regression estimator that, in contrast to many existing methods, does not rely on local smoothness assumptions nor is it constructed using local smoothing techniques. Instead, our estimator respects global smoothness constraints by virtue of falling in a class of right-hand continuous functions with left-hand limits that have variation norm bounded by a constant. Using empirical process theory, we establish a fast minimal rate of convergence of our proposed estimator and illustrate how such an estimator can be constructed using standard software. In simulations, we show that the finite-sample performance of our estimator is competitive with other popular machine learning techniques across a variety of data generating mechanisms. We also illustrate competitive performance in real data examples using several publicly available data sets.
回归函数的估计是统计学习的一个常见目标。我们提出了一种新颖的非参数回归估计器，与许多现有方法不同，它既不依赖局部平滑假设，也不是使用局部平滑技术构建的。相反，我们的估计器通过属于一类右连续且具有左极限的函数来尊重全局平滑约束，这些函数的变差范数由一个常数界定。利用经验过程理论，我们建立了所提出估计器的快速最小收敛速率，并说明了如何使用标准软件构建这样的估计器。在模拟中，我们表明，在各种数据生成机制下，我们估计器的有限样本性能与其他流行的机器学习技术具有竞争力。我们还使用几个公开可用的数据集在实际数据示例中展示了其具有竞争力的性能。
