Data Adaptive Ridging in Local Polynomial Regression
Data Adaptive Ridging in Local Polynomial Regression
复制标题
局部多项式回归中的数据自适应脊化
DOI：
10.1080/10618600.2000.10474884
复制
发表时间：
2000
影响因子：
2.4
通讯作者：
T. Gasser
中科院分区：
文献类型：
--
作者：
B. Seifert;T. Gasser
摘要在估计回归函数或其导数时，局部多项式由于其灵活性和渐近性能而成为一种有吸引力的选择。Seifert和Gasser提出了局部多项式的脊化，以克服随机设计的方差问题，同时保留其优点。在这篇文章中，我们提出了一个数据独立的经验法则和数据自适应的局部线性回归中的脊参数的空间选择。在惩罚局部最小二乘回归的框架下，该方法被推广到高阶多项式、导数估计和多元设计。主要的信息是，脊是一个强大的工具，提高当地多项式的性能。经验法则提供了巨大的改进;数据自适应脊带来了进一步但适度的均方误差增益。
Abstract When estimating a regression function or its derivatives, local polynomials are an attractive choice due to their flexibility and asymptotic performance. Seifert and Gasser proposed ridging of local polynomials to overcome problems with variance for random design while retaining their advantages. In this article we present a data-independent rule of thumb and a data-adaptive spatial choice of the ridge parameter in local linear regression. In a framework of penalized local least squares regression, the methods are generalized to higher order polynomials, to estimation of derivatives, and to multivariate designs. The main message is that ridging is a powerful tool for improving the performance of local polynomials. A rule of thumb offers drastic improvements; data-adaptive ridging brings further but modest gains in mean square error.