非参数自回归函数的有限元估计及其收敛速度

针对局部方法不能给出所拟合模型的简单的显式表达式,而且拟合和预报的计算量较大,本文考虑一种估计非参数自回归函数的全局有限元方法。该方法不但能克服上述局部方法之不足,而且在一定情形下优于多项式样条方法。在α-混合条件下得出了非参数自回归函数有限元估计的收敛速度,同时给出了利用AIC准则自动选择结点个数的数据追赶法,模拟算例说明了有限元估计方法的可行性。

Finite Element Estimate for Nonparametric Autoregressive Functions and its Convergence Rate

A global finite element estimation for nonparametric autoregressive functions is considered in this paper, due primarily to the fact that local smoothing methods fail to offer a parsimonious explicit expression of the fitted model and in order to fit and predict easily. The global method not only overcomes the limitations of the local methods mentioned above, but also outperforms the polynomial spline method in some cases. Under the a-mixing condition, the convergence rate of the finite element estimator for nonparametric autoregressive functions is established. Meanwhile, a datadriven procedure for automatic selection of knot number is provided based on the AIC criterion. The feasibility of the finite element estimation is demonstrated by simulation examples.