固定设计异方差非参数回归模型的预测方法

Prediction Methods for Nonparametric Regression Models with Fixed Design and Heteroscedasticity

文章针对固定设计下异方差非参数回归模型,考虑了基于多项式样条的三种预测方法,即非外推法、线性外推法和非线性外推法。模拟结果表明非外推预测法的均方根误差(RMSE)和平均绝对误差(MAE)的均值最大,而线性外推法的RMSE和MAE的均值略小于非线性外推法的RMSE和MAE的均值。实证分析结果显示:非外推预测法的平均绝对百分比误差(MAPE)、RMSE和MAE最大,线性外推法的MAPE、RMSE和MAE最小。这表明整体上外推法优于非外推法,而线性外推法是简单可行的。

Aimed at nonparametric regression models with fixed design and heteroscedastic errors, this paper considers three prediction methods based on polynomial spline, i.e. non-extrapolation method, linear extrapolation method and nonlinear extrapolation method. Simulation results show that the average values of root mean squared error （RMSE） and mean absolute error （MAE） of non-extrapolation method are the biggest; while the average values of RMSE and MAE of linear extrapolation method are slightly smaller than those of nonlinear extrapolation method. The empirical analysis result indicates that the non-extrapolation method gives the biggest mean absolute percentage error （MAPE）, RMSE and MAE, and the MAPE, RMSE and MAE of linear extrapolation method are the smallest ones, which suggests that on the whole the extrapolation methods outperform the non-extrapolation method, and that the linear extrapolation is a simple and feasible method.