| 鞅差序列的Bernstein型不等式及其应用 |
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| 引用本文： | 李国亮.鞅差序列的Bernstein型不等式及其应用[J].数学杂志,2006,26(1):103-108. |
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| 作者姓名： | 李国亮 |
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| 作者单位： | 武汉大学数学与统计学院,湖北,武汉,430072 |
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| 基金项目： | 国家自然科学基金资助项目(10371092). |
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| 摘 要： | 本文将独立随机变量序列的Bernstein型不等式推广到鞅差序列情形,给出该不等式的一个应用,并在一定条件下证明了非参数回归中函数估计的强相合性.
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| 关 键 词： | 鞅差序列 Bernstein型不等式 |
| 文章编号： | 0255-7797（2006）01-0103-06 |
| 收稿时间： | 2004-11-16 |
| 修稿时间： | 2004-11-162005-06-30 |
BERNSTEIN INEQUALITY OF THE SEQUENCE OF MARTINGALE DIFFERENCES AND ITS APPLICATIONS |
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| LI Guo-liang.BERNSTEIN INEQUALITY OF THE SEQUENCE OF MARTINGALE DIFFERENCES AND ITS APPLICATIONS[J].Journal of Mathematics,2006,26(1):103-108. |
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| Authors: | LI Guo-liang |
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| Institution: | School of Math. and Statistics, Wuhan University , Wuhan 430072 China |
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| Abstract: | In this paper we generalize Bernstein inequality of t he sequence of independent random variables to the martingale differences, then we give an application of this inequality.Under some assumptions, we prove the s trong consistency of the function estimate of the nonparametric regressions. |
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| Keywords: | martingale difference Bernstein inequality |
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