| 基于方向数据的核密度估计的对称检验的大偏差 |
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| 引用本文： | 徐明周,程琨.基于方向数据的核密度估计的对称检验的大偏差[J].数学研究及应用,2021,41(6):639-647. |
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| 作者姓名： | 徐明周 程琨 |
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| 作者单位： | 景德镇陶瓷大学信息工程学院, 江西 景德镇 333403 |
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| 基金项目： | 景德镇陶瓷大学博士科研启动项目(Grant No.102/01003002031),江西省教育厅科学技术项目(Grant Nos.GJJ190732; GJJ180737), 江西省自然科学基金(Grant No.20202BABL211005). |
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| 摘 要： | 设$f_n$是基于核函数$K$和取值于$d$-维单位球面${\mathbb{S}}^{d-1}$的独立同分布随机变量列的非参数核密度估计. 我们证明了若核函数是有界变差函数, 随机变量的密度函数$f$是连续的和对称的, $\{\sup_{x\in {\mathbb{SS}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$的大偏差原理成立.
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| 关 键 词： | 对称检验 核密度估计 方向数据 大偏差 |
| 收稿时间： | 2020/10/19 0:00:00 |
| 修稿时间： | 2021/5/20 0:00:00 |
Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data |
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| Mingzhou XU,Kun CHENG.Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data[J].Journal of Mathematical Research with Applications,2021,41(6):639-647. |
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| Authors: | Mingzhou XU Kun CHENG |
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| Institution: | School of Information Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China |
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| Abstract: | Assume that $f_n$ is the nonparametric kernel density estimator of directional data based on a kernel function $K$ and a sequence of independent and identically distributed random variables taking values in $d$-dimensional unit sphere ${\mathbb{S}}^{d-1}$. We established that the large deviation principle for $\{\sup_{x\in {\mathbb{S}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$ holds if the kernel function is a function with bounded variation, and the density function $f$ of the random variables is continuous and symmetric. |
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| Keywords: | symmetry test kernel density estimator directional data large deviations |
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