| 两类相依样本密度函数核估计的相合性 |
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| 引用本文： | 胡学平.两类相依样本密度函数核估计的相合性[J].吉林大学学报(理学版),2013,51(6):1085-1089. |
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| 作者姓名： | 胡学平 |
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| 作者单位： | 安庆师范学院 数学与计算科学学院, 安徽 安庆 246133 |
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| 摘 要： | 设{Xn,n≥1}为同分布的NOD随机序列或严平稳的m相依序列, f(x)为随机变量X1的概率密度函数. 基于样本X1,X2,…,Xn, 利用Fourier变换及NOD列的性质和相关指数不等式, 研究密度函数f(x)的核估计, 在适当的条件下得到了KG-*4]f(x)核估计的逐点强相合性、 r阶相合性及依概率一致收敛性.
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| 关 键 词： | NOD样本 m相依样本 核估计 强相合性 r阶相合性 |
| 收稿时间： | 2012-10-22 |
Consistency of Kernel Type Density Estimations ofTwoSorts of Dependent Samples |
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| HU Xue ping.Consistency of Kernel Type Density Estimations ofTwoSorts of Dependent Samples[J].Journal of Jilin University: Sci Ed,2013,51(6):1085-1089. |
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| Authors: | HU Xue ping |
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| Institution: | School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, Anhui Province, China |
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| Abstract: | Let {Xn,n≥1} be an identically distributed NOD random sequence or a strict stationary sequence of m dependent random variables, and f(x) is a probability density function of random variable X1. Based on NOD samples or m dependent samples, under suitable conditions the kernel estimator for density function f(x) was investigated, and the pointwise strong consistency, the consistency in r order mean and uniform consistency in L1 were obtained via Fourier transform, the related properties for NOD random sequences and the exponential inequality. |
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| Keywords: | NOD samples m dependent samples kernel estimator strong consistency consistency in r order mean |
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