PLUG‐IN ESTIMATION OF GENERAL LEVEL SETS
PLUG‐IN ESTIMATION OF GENERAL LEVEL SETS
复制标题
通用水平集的插件估计
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Rodríguez
中科院分区：
文献类型：
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作者：
A. Cuevas;W. González;A. Rodríguez
给定一个未知函数(例如，概率密度、回归函数、…)F和一个常数c，考虑水平集L(C)={f≥c}的估计问题。这个问题是在一个非常通用的框架中解决的，它允许在不同于的度量空间上定义f。这种程度的普遍性是出于实际考虑，事实上，用天文数据分析了一个例子，其中f的域是单位球面。用插入法估计L(C)，Ln(C)={fn≥c}，其中fn是f的估计量.得到了关于∂Ln(C)的边界关于Hausdorff度量的相合性和收敛速度的两个结果.∂L(C).在较弱的条件下，证明了Ln(C)与L(C)关于L1距离的相合性。对球面数据的特殊情况给予了特别关注。
Given an unknown function (e.g. a probability density, a regression function, …) f and a constant c, the problem of estimating the level set L(c) ={f≥c} is considered. This problem is tackled in a very general framework, which allows f to be defined on a metric space different from . Such a degree of generality is motivated by practical considerations and, in fact, an example with astronomical data is analyzed where the domain of f is the unit sphere. A plug‐in approach is followed; that is, L(c) is estimated by Ln(c) ={fn≥c}, where fn is an estimator of f. Two results are obtained concerning consistency and convergence rates, with respect to the Hausdorff metric, of the boundaries ∂Ln(c) towards ∂L(c). Also, the consistency of Ln(c) to L(c) is shown, under mild conditions, with respect to the L1 distance. Special attention is paid to the particular case of spherical data.