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混合序列矩不等式和非参数估计
引用本文:杨善朝.混合序列矩不等式和非参数估计[J].数学学报,1997,40(2):271-279.
作者姓名:杨善朝
作者单位:广西师范大学数学与计算机科学系 桂林541004
摘    要:对p-混合、(?)-混合序列给出两个矩不等式,它们在加权和序列研究中比邵启满在6]、7]中给出的矩不等式更实用.作为应用,这里讨论非参数递归密度核估计的强收敛速度和非参数回归函数加权核估计的强相合性,获得较好结论.

关 键 词:混合序列  矩不等式  递归密度核估计回归函数加权核估计  强收敛性
收稿时间:1995-5-23
修稿时间:1996-4-9

Moment Inequality for Mixing Sequences and Nonparametric Estimation
Yang Shanchao.Moment Inequality for Mixing Sequences and Nonparametric Estimation[J].Acta Mathematica Sinica,1997,40(2):271-279.
Authors:Yang Shanchao
Institution:Yang Shanchao (Department of Mathematics and Computer Science, Guangxi Normal University, Guilin 541004, China)
Abstract:This paper gives two moment inequalities for σ-mixing and (ψ-mixing sequences. In the study of weighted sums, they are more useful than ones abtained by Shao Qiman in 6] and 7]. Here they are applied to discuss the rate of strong convergence for the nonparametric recursive kernel estimators and the strong consistency for the nonparametric weighted kernel estimators of regression function. The obtained results are much better.
Keywords:Mixing sequence  Moment inequality  Recursive kernel estimator  Kernel estimator of regression function  Strong convergence
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