摘要
针对局部线性估计方法收敛速度较慢且对窗宽选择不稳健的问题,本文提出一种改进的局部线性半参估计方法.首先,选择不同窗宽作相应的局部线性估计,然后利用这些估计构造参数回归模型,由此给出回归函数的参数估计.相对于局部线性估计,新方法在不改变方差阶的情况下,将估计偏差的阶由h2减小至h4,最优均方收敛速度提高至O(n-8/9),且对窗宽选择稳健.模拟研究验证了新方法的有效性.
To improve the convergence rate and the robustness of bandwidth selection of the local linear estimation, an improved semi-parametric estimation is proposed in this paper. At first, several local linear estimators with different bandwidths are carried out, and then combined by a parametric regression technique to construct an improved one. Compared with the ordinary local linear estimator, the asymptotic bias of the new estimator can be reduced from an order of h2 to h4 without changing the order of asymptotic variance. Consequently, the optimal convergence rate of such estimator can attain O（n-8/9） which is also robust to the selection of bandwidth. Numerical simulations show that the new approach outperform the local linear estimator.
出处
《工程数学学报》
CSCD
北大核心
2013年第5期695-701,共7页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(6097408)
中央高校基本科研业务费专项资金(K50510700007)~~
关键词
非参数回归
均方误差
窗宽选择
稳健
nonparametric regression
mean square error
bandwidth selection
robustness
