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基于平稳α-混合左删失数据众数核估计的渐近正态性

Asymptotic normality of kernel mode estimator under left-truncated and stationary α-mixing sequence
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摘要 文章研究了基于平稳α-混合左删失数据下密度函数一阶、二阶导数的核估计及众数核估计,在一定的条件下获得了导数核估计量的强一致收敛性、收敛速度及众数核估计量的渐近正态性;同时给出了众数估计的置信区间,最后,通过数据模拟显示了主要结论的合理性。 The kernel estimator of the first and second derivative of density function and the kernel mode estimators under left-truncated and stationary a-mixing sequence are studied. The strong uni- form convergence and convergence rate of kernel estimator of the first and second derivative of density function are got, and the asymptotic normality of the kernel mode estimators under left-truncated and stationary a-mixing sequence is also obtained under certain conditions. Then the confidence interval of the mode estimator is presented. The numerical simulation demonstrates the rationality of the main conclusions in this paper.
作者 李成好 汪超 凌能祥
机构地区 合肥工业大学数学学院
出处 《合肥工业大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第8期1145-1152,共8页 Journal of Hefei University of Technology：Natural Science
基金 安徽省自然科学基金资助项目(11040606M03) 教育部科学研究重大资助项目(309017) 教育部人文社科规划基金资助项目(10YJA910005) 安徽省教育厅重点基金资助项目(KJ2010A282) 合肥工业大学研究生精品课程建设资助项目(YJK2010Z01)
关键词 渐近正态 删失数据 Α-混合 众数 核估计 置信区间 asymptotic normality truncated data a-mixing mode kernel estimator confidence inter-val
分类号 O212.7 [理学—概率论与数理统计]
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参考文献18

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合肥工业大学学报（自然科学版）
2012年 第8期

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