Generalized jackknifing and higher order kernels
Generalized jackknifing and higher order kernels
复制标题
广义折刀和高阶内核
DOI：
10.1080/10485259308832573
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
P. Foster
中科院分区：
文献类型：
--
作者：
M. C. Jones;P. Foster
至少在理论上，提高概率密度、回归函数和谱密度等曲线的核估计器性能的一种方法是使用“高阶”核函数。在本文中，我们研究了如何从低阶核获得高阶核，并在广义折刀的统一概念下提出了各种现有的和新颖的公式（Schucany、Gray 和 Owen，1971）。因此，我们极大地扩展了 Schucany 和 Sommers (1977) 的方法。副产品包括与更“直接”偏差校正方法的链接，对例如 Gasser、Muller 和 Mammitzsch (1985) 的“最佳”多项式核如何相互关联的简化理解，与 Wand 和 Schucany (1990) 的基于高斯的核的连接，以及 Terrell 和 Scott (1980) 的基于高阶核思想的估计中强制非负性的方法的许多扩展。
One way of improving the performance, at least in theory, of kernel estimators of curves such as probability densities, regression functions and spectral densities is to use “higher order” kernel functions. In this paper, we investigate how one might obtain higher order kernels from lower.order ones, and put forward a wide variety of existing and novel formulae under the unifying concept of generalized jackknifing (Schucany, Gray and Owen, 1971). We thus greatly expand on the approach of Schucany and Sommers (1977). Spinoffs include links with more “direct” bias correction methods, a simplified understanding of how the “optimal” polynomial kernels of, for example, Gasser, Muller and Mammitzsch (1985) relate to one another, connections with the Gaussian-based kernels of Wand and Schucany (1990), and many extensions of Terrell and Scott's (1980) method of enforcing nonnegativity in estimates based on higher order kernel ideas.