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基于相依函数型数据条件均值函数估计的渐近性质 被引量：2

Asymptotic property of conditional mean estimation with dependent functional data
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摘要 文章利用熵的方法研究了基于函数型数据的条件均值函数估计的一致收敛速度,在一定条件下获得了基于相依函数型数据的条件均值函数估计量的几乎完全一致收敛速度,推广了i.i.d场合下或某些相依情形下的的逐点收敛速度。 In this paper,the uniform convergence rate for conditional mean estimation with functional data is investigated by the Kolmogorov＇s entropy.Under certain conditions,the uniform almost complete convergence rate for conditional mean estimator with dependent functional data is established which extends the pointwise convergence rate in i.i.d or in some dependent cases.
作者 丁洁 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 2011年第7期1104-1107,1116,共5页 Journal of Hefei University of Technology：Natural Science
基金 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) 安徽省自然科学基金资助项目(11040606M03)
关键词 α混合 函数型数据 熵 几乎完全一致收敛速度 α-mixing functional data entropy uniform almost complete convergence rate
分类号 O212.7 [理学—概率论与数理统计]
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参考文献9

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同被引文献28

  • 1Louani D. On the asymptotic normality of the kernel esti- mators of the density function and its derivatives under cen- soring[J]. Comm Stat Theor Meth, 1998,27 : 2909- 2924.
  • 2Ould-Said E, Cai Z W. Strong uniform consistency of non- parametric estimation of the censored conditional mode function[J]. Journal of Nonparametr Stat, 2005, 17 (7) : 797-806.
  • 3Cai Z W. Asymptotic properties of Kaplan-Meier estimatorfor censored dependent data [J]. Star Probab Lett, 1998, 37:381-389.
  • 4Cai Z W. Estimating a distribution function for censored time series data [J]. Journal of Multivariate Anal. 2001,78 : 299:318.
  • 5Ould-Said E,Tatachak A. On the nonparametric estimation of mode under left truncated model, Technical Report L M P A 2005,No. 271[R]. Univ du Littoral cote d'Ople, 2005.
  • 6OuId-Sa[d E, Tatachak A. Asymptotic properties of the ker- nel estimator of the condiiional mode for the left truncated model[J]. Statistics : Probability Letters, 2007, 344: 651-656.
  • 7Ould-Said,TatachakA. Strong consistency rate for the ker- nel mode estimator under strong mixing hypothe:s and left truncation [ J ]. Comm Stat Theo Meth, 2009, 38: 1154-1169.
  • 8Khardani S, Lemdani M, Ould-Said E. On the strong uni- form consistency of the mode estimator for censored time series[J]. Metrika, 2012,75 : 229- 241.
  • 9Liang Hanying, de Una-A' lvarez J. Asymptotic normality for estimator of conditional mode under left-truncated and dependent observations[J]. Metrika, 2010,72 : 1 - 19.
  • 10Stute W. Almost sure representation of the product-limit estimator for truncated data [J]. Ann Statist, 1993, 21: 146-156.

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合肥工业大学学报（自然科学版）
2011年 第7期

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