| 引用本文: | 陈性敏,高超.递推局部线性回归估计及其应用[J].控制理论与应用,2013,30(4):482~491.[点击复制] |
| CHEN Xing-min,GAO Chao.Recursive local linear regression estimation and its applications[J].Control Theory and Technology,2013,30(4):482~491.[点击复制] |
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| 递推局部线性回归估计及其应用 |
| Recursive local linear regression estimation and its applications |
| 摘要点击 4019 全文点击 2273 投稿时间：2012-10-18 修订日期：2013-01-07 |
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| DOI编号 10.7641/CTA.2013.21076 |
| 2013,30(4):482-491 |
| 中文关键词 局部线性回归 递推辨识 核估计 强一致性 非线性ARX系统 |
| 英文关键词 local linear regression recursive identification kernel estimation strong consistency nonlinear ARX systems |
| 基金项目 国家自然科学基金资助项目(61203118); 中央高校基本科研业务费专项资金资助项目. |
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| 中文摘要 |
| 在非参数统计中, 局部多项式回归是重要的工具, 然而以往研究的算法基本都是非递推的. 本文研究递推的局部线性回归估计及其应用. 首先推导出递推算法, 给出了回归函数及其导函数的非参数估计. 在一定的条件下, 证明了算法的强一致性. 并且通过仿真例子研究了它在非线性条件异方差模型的回归函数估计和非线性ARX(nonlinear autoregressive system with exogenous inputs, NARX)系统辨识中的应用. |
| 英文摘要 |
| In nonparametric statistics, local polynomial regression is one of the most important tools. However, almost the previous work is based on nonrecursive algorithms. We investigate the recursive local linear regression estimation. The recursive algorithms are derived for the nonparametric estimation of the regression function and its derivative. Strong consistence of the estimates is established under reasonable conditions. The applications to estimation of the regression model with nonlinear conditional heteroskedasticity and identification of the nonlinear ARX (NARX) system are demonstrated by numerical simulation. |