| 正交级数密度估计积分平方误差的极限定理 |
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| 引用本文： | 吴成庆,赵林城. 正交级数密度估计积分平方误差的极限定理[J]. 中国科学技术大学学报, 2001, 31(4): 407-411 |
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| 作者姓名： | 吴成庆 赵林城 |
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| 作者单位： | 中国科学技术大学统计与金融系,安徽合肥,230026 |
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| 基金项目： | Research partiallysupported by National Natur al Science Foundation of China(19631040; 19971085), Ph.D.Program Foundation of Ministry of Education of China and Special Foundation of AcademiaSinica |
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| 摘 要： | 论文研究了密度函数正交级数的积分平方误差（ISE）的渐近性质。在相当弱的条件下，证明了ISE正则化后的渐近分布等同于一列独立的中心化后的χ^21随机变量的线性组合的分布。
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| 关 键 词： | 中心极限定理 正交级数 密度估计 积分平方误差 正则化 渐近分布 密度函数 |
| 文章编号： | 0253-2778(2001)04-0407-05 |
Limit Theorem forIntegrated Square Error of Orthogonal Series Density Estimators |
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| Abstract. Limit Theorem forIntegrated Square Error of Orthogonal Series Density Estimators[J]. Journal of University of Science and Technology of China, 2001, 31(4): 407-411 |
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| Authors: | Abstract |
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| Abstract: | The limiting distribution for is derived integrated square error(ISE) of nonparametric density estimators based on orth ogonal series under some mild conditions, and it is proved that the limiting dis tributi on of the standardization of ISE is the distribution of a linear combination of independent centred χ21 random variables. |
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| Keywords: | central limittheorem orthogonal series density est imate integrated square error |
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