Data Sharpening for Nonparametric Inference Subject to Constraints
Data Sharpening for Nonparametric Inference Subject to Constraints
复制标题
受约束的非参数推理的数据锐化
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
P. Hall
中科院分区：
文献类型：
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作者：
W. J. Braun;P. Hall
数据锐化包括干扰数据以提高统计方法的性能。过去提出的版本都是为了减少曲线估计中的偏差，并且每个基准点的摄动量都是由一个显式确定的。本文提出了一种基于距离的数据锐化形式，在对估计器施加约束的情况下，数据移动的距离之和被最小化。约束可能导致偏差减少，或导致方差或变异性减少，或导致曲线估计量是单调或单峰的。与早期版本的方法不同，在本文给出的形式中，锐化量和锐化程度由一个公式隐式确定，该公式通常作为拉格朗日乘子方程的解给出。有时可以通过牛顿-拉夫森迭代找到解，尽管当施加定性约束时，通常需要二次规划或相关方法。
Data sharpening involves perturbing the data to improve the performance of a statistical method. The versions of it that have been proposed in the past have been for bias reduction in curve estimation, and the amount of perturbation of each datum has been determined by an explicit formula. This article suggests a distance-based form of data sharpening, in which the sum of the distances that data are moved is minimized subject to a constraint imposed on an estimator. The constraint could be one that leads to bias reduction, or to variance or variability reduction, or to a curve estimator being monotone or unimodal. In contrast to earlier versions of the method, in the form presented in this article the amount and extent of sharpening is determined implicitly by a formula that is typically given as the solution of a Lagrange-multiplier equation. Sometimes the solution can be found by Newton–Raphson iteration, although when qualitative constraints are imposed it usually requires quadratic programming or a related method.