徐明周, 丁云正, 周永正. 核密度估计的对称检验在~$L_1(\mathbb{R}^d)$~下的中偏差[J]. 应用概率统计, 2019, 35(2): 141-152. DOI: 10.3969/j.issn.1001-4268.2019.02.003
引用本文: 徐明周, 丁云正, 周永正. 核密度估计的对称检验在~$L_1(\mathbb{R}^d)$~下的中偏差[J]. 应用概率统计, 2019, 35(2): 141-152. DOI: 10.3969/j.issn.1001-4268.2019.02.003
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XU Mingzhou, DING Yunzheng, ZHOU Yongzheng. Moderate Deviations in L_1(\mathbb{R}^d) for a Test of Symmetry Based on Kernel Density Estimator[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(2): 141-152. DOI: 10.3969/j.issn.1001-4268.2019.02.003
Citation: XU Mingzhou, DING Yunzheng, ZHOU Yongzheng. Moderate Deviations in L_1(\mathbb{R}^d) for a Test of Symmetry Based on Kernel Density Estimator[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(2): 141-152. DOI: 10.3969/j.issn.1001-4268.2019.02.003
shu

核密度估计的对称检验在~L_1(\mathbbR^d)~下的中偏差

Moderate Deviations in L_1(\mathbbR^d) for a Test of Symmetry Based on Kernel Density Estimator

    摘要
  • 摘要: 设f_n是基于一个核函数K和取值于\mathbbR^d的独立同分布随机变量列的一个非参数核密度估计. 本文证明了f_n(x)-f_n(-x),\, n\ge1\在L_1(\mathbbR^d)空间下的两个中偏差定理.

     

    Abstract: Let f_n be a non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in \mathbbR^d. In this paper we prove two moderate deviation theorems in L_1(\mathbbR^d) for \f_n(x)-f_n(-x),\,n\ge1\.

     

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