鞅差误差下非参数方差模型的样条估计

Spline Estimation for Nonparametric Variance Models Under Martingale Difference Errors

考虑固定设计和鞅差误差下的非参数方差模型,利用多项式样条方法,得到了非参数方差函数估计的最优全局收敛速度和一致收敛速度。模拟算例不仅说明了样条估计方法的可行性,而且其拟合效果和估计性质在一定条件下还优于局部线性方法。

Nonparametric variance models with fixed design and martingale difference errors were considered in this paper.Based on polynomial spline method,consistent results for the estimator of variance function were discussed.Optimal global rate of convergence and uniform rate of convergence were obtained.Also,the feasibility of the spline estimation was illustrated by a simulation example.The results shows that the spline method outperforms the local linear method on the behavior of fitness and unbiased estimate under certain circumstances.