It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this paper we propose a new sliced least-squares estimator that utilizes ideas from Sliced Inverse Regression. Slices with problematic observations that contribute to high variability in the estimator can easily be down-weighted to robustify the procedure. The estimator is simple to implement and can result in vast improvements for some models when compared to the usual least-squares approach. While the estimator was initially conceived with the single-index model in mind, we also show that multiple directions can be obtained, therefore providing another notable advantage of using slicing with least squares. Several simulation studies and a real data example are included, as well as some comparisons with some other recent methods.
翻译:先前已经表明,普通最小方块可以仅在温和条件下用于估计单指数模型的系数。 但是, 估计值是非野蛮的, 导致某些模型的估计数差。 在本文中, 我们提出一个新的切片最小方块估计值, 使用从剪切反反反反反反反反反反反反反反向的理念。 具有导致估计值差异的有问题观测结果的切片很容易被下沉加权, 以强化程序。 估计值是易于执行的, 并可能导致某些模型与通常的最小方块方法相比大有改进。 虽然估计值最初是用单一指数模型设计的, 我们还表明可以取得多个方向, 从而提供了使用最小方块的剪切的另一个显著优势。 包含一些模拟研究和真实数据实例, 并与最近的一些方法进行了一些比较。