基于样条估计的非参数方差模型的区间预测

Interval Prediction of Nonparametric Variance Models Based on Spline Estimation

摘要: 为了探寻固定设计下非参数方差模型的区间预测问题，基于方差函数的多项式样条估计和线性外推法，构建了响应变量数据的预测区间。数值模拟算例表明：随着样本容量的增加，平均区间覆盖率逐渐接近给定的置信水平，预测的平均区间宽度逐渐减小；在节点个数选择上，AIC准则优于BIC准则。此外，对河南省第三产业贡献率数据进行了应用分析，得到了“十五五”时期的预测区间。

Abstract: In order to solve the problem of interval prediction of nonparametric variance models with fixed design, a prediction interval of response variable is constructed by the polynomial spline estimate of variance function and the linear extrapolation in this paper. The results of a simulation example show that as the sample size increases, the average interval coverage rate gradually approaches the given confidence level, and the average width of the prediction intervals gradually decreases. In terms of knot number selection, the AIC criterion outperforms the BIC criterion. Furthermore, an application analysis is conducted on the contribution rate of the tertiary industry to the increase of the GDP in Henan province. And the prediction intervals for the 15^th Five-Year Plan period are obtained.