强相关数据回归函数的小波估计

李林元; 肖益民

强相关数据回归函数的小波估计

李林元¹,
肖益民²

1.
美国新罕布什尔大学数理统计系,美国 000;2.美国密执安州立大学统计和概率系,美国 000

详细信息

作者简介:
李林元(1965- ),男,江苏人,副教授,博士(联系人.E-mail:linyuan@math.unh.edu).

中图分类号: O212.7
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- 被引次数: 0
出版历程
- 收稿日期: 2005-01-17
- 修回日期: 2006-04-09
- 刊出日期: 2006-07-15

Wavelet-Based Estimators of the Mean Regression Function With Long Memory Date

LI Lin-yuan¹,
XIAO Yi-min²

1.
Department of Mathematics and Statistics, University of New Hampshire, USA;

摘要

摘要: 讨论了在强相关数据情形下对回归函数的小波估计，并且给出了估计量的均方误差的一个渐近展开表示式．对研究估计量的优劣，所推导的近似表示式显得非常重要．对一般的回归函数核估计，如果回归函数不是充分光滑，这个均方误差表示式并不成立A·D2但对小波估计，即使回归函数间断连续，这个均方误差表示式仍然成立．因此，小波估计的收敛速度要比核估计来得快，从而小波估计在某种程度上改进了现有的核估计．
- 均方误差 /
- 非参数回归 /
- 小波估计 /
- 收敛率
Abstract: An asymptotic expansion is provide for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion is shown, when the underlying mean regression function is only piecewise smooth. It is the same with analogous expansion for the kernel estimators. However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.
- mean integrated square error /
- nonparametric regression /
- nonlinear wavelet-based estimator /
- rate of convergence

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参考文献(25)

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