函数型数据的近邻域估计

邢文杰, 王立洪

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 339-350.

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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 339-350. DOI: 10.12386/A2014sxxb0034
论文

函数型数据的近邻域估计

    邢文杰, 王立洪
作者信息 +

Nearest Neighbor Estimation for Functional Data

    Wen Jie XING, Li Hong WANG
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文章历史 +

摘要

主要讨论函数型数据的近邻域估计的渐近性质.在α-混合条件及一些正则性假设下,我们讨论了函数空间上非参数回归函数的k阶近邻域估计的相合性和渐近正态性.通过模拟分析几组不同误差分布的函数型数据,并与核估计方法进行比较,验证了有限样本下,近邻域估计方法的有效性,并得出 近邻域估计在稳健性方面更有优势.

Abstract

We consider the asymptotic properties of the nearest neighbor estimation for functional data. Under α-mixing and some regularity assumptions, we investigate the consistency and asymptotic normality of the nearest neighbor estimation for the nonparametric regression models with functional data. For the empirical data analysis, we consider three different distributions of the errors. The results show that the advantages of the nearest neighbor estimation lie in its easy computation, robustness and good performance under finite sample.

关键词

函数型数据 / k阶近邻域估计 / α-混合 / 相合性

Key words

functional data / nearest neighbor estimation / α-mixing / consistency

引用本文

导出引用
邢文杰, 王立洪. 函数型数据的近邻域估计. 数学学报, 2014, 57(2): 339-350 https://doi.org/10.12386/A2014sxxb0034
Wen Jie XING, Li Hong WANG. Nearest Neighbor Estimation for Functional Data. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 339-350 https://doi.org/10.12386/A2014sxxb0034

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基金

国家自然科学基金(11171147);教育部高等学校科技创新工程重大项目培育资金(708044);江苏省青蓝工程资助项目
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