Variance Properties of Local Polynomials and Ensuing Modifications
Variance Properties of Local Polynomials and Ensuing Modifications
复制标题
局部多项式的方差性质及随后的修改
DOI：
10.1007/978-3-642-48425-4_3
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
T. Gasser
中科院分区：
文献类型：
--
作者：
B. Seifert;T. Gasser
局部多项式回归估计有很多优点，有可能成为曲线拟合的“黄金标准”。吸引人的理论特征与随机设计的方差性质和实际经验是部分矛盾的。条件方差是无界的。当使用最优(紧凑)权重时，无条件方差是无限的。关于核和局部多项式估计器的权重构造的教程说明了这些问题的机理。高斯权重的属性更好，但计算速度较慢。我们展示了数值不稳定性和统计不稳定性之间的联系以及相应的解决方案。在这种情况下，k-近邻规则被证明是不适当的工具。利用方差-偏差折衷和局部多项式岭回归，我们提出了一种改进的局部带宽调制。
Local polynomial regression estimation has a number of advantages and might become a “golden standard” for curve fitting. The attractive theoretical features are in partial contradiction to variance properties for random design and to practical experience. The conditional variance is unbounded. The unconditional variance is infinite when using optimal (compact) weights. A tutorial illustration of construction of weights for kernel and local polynomial estimators clarifies the mechanism of these problems. Properties are better for Gaussian weights, which are, however, computationally slow. We show the connection between numerical and statistical instabilities and corresponding solutions. Thek-nearest-neighbour rule is shown to be an inadequate tool in this context. We propose a refined local modulation of bandwidth using a variance-bias compromise and local polynomial ridge regression.