论文标题
预测回归深度的精确计算以及其诱导的中位数和其他估计器的快速计算
Exact computation of projection regression depth and fast computation of its induced median and other estimators
论文作者
论文摘要
Zuo（2019）（Z19）解决了投影回归深度（PRD）及其诱导中位数（最大深度估计量）的计算。 Z19通过常规单变量样品中位数的修改版本实现了PRD的确切计算，从而导致PRD不变性损失和深度诱导的中位数的等效性。本文实现了确切的计算，而不会吓到PRD的不变性和回归中位数的均衡性。 Z19还解决了PRD诱导的中位数的近似计算，Z19中的天真算法非常慢。本文修改了Z19中的近似值，并采用RCPP软件包，因此获得了更快的算法（可能是$ 100 $ $ $乘以），同时准确性更高。此外，作为第三个主要贡献，本文介绍了三个新的深度引起的估计器，这些估计量的运行速度可能比Z19的$ 300 $倍，同时保持相同（或更好）的准确性水平。提出了真实和模拟的数据示例，以说明Z19算法与本文提出的算法之间的差异。调查结果支持上面的陈述并表现出本文的主要贡献。
Zuo (2019) (Z19) addressed the computation of the projection regression depth (PRD) and its induced median (the maximum depth estimator). Z19 achieved the exact computation of PRD via a modified version of regular univariate sample median, which resulted in the loss of invariance of PRD and the equivariance of depth induced median. This article achieves the exact computation without scarifying the invariance of PRD and the equivariance of the regression median. Z19 also addressed the approximate computation of PRD induced median, the naive algorithm in Z19 is very slow. This article modifies the approximation in Z19 and adopts Rcpp package and consequently obtains a much (could be $100$ times) faster algorithm with an even better level of accuracy meanwhile. Furthermore, as the third major contribution, this article introduces three new depth induced estimators which can run $300$ times faster than that of Z19 meanwhile maintaining the same (or a bit better) level of accuracy. Real as well as simulated data examples are presented to illustrate the difference between the algorithms of Z19 and the ones proposed in this article. Findings support the statements above and manifest the major contributions of the article.
