t分布误差下非参数回归模型的区间估计

Interval Estimation of Non-Parametric Regression Model with t Distribution Error

摘要: 为了探索非正态分布误差下非参数回归模型的区间估计问题，本文考虑了模型误差独立且服从t分布的情形。利用小波方法和t分布的性质，构建响应变量的近似置信区间。考虑到在应用中误差分布未知，利用Bootstrap采样得到原始信号数据的区间估计。模拟算例表明：在区间覆盖率、区间平均带宽和覆盖宽度准则意义下，与基于重构信号的区间估计相比较，基于近似信号的区间估计是一种较为理想的方法。

Abstract: In order to explore the interval estimation problem of non-parametric regression model under non-normal distribution error, the case of independent and t distribution errors is considered in this paper. The approximate confidence interval of response variable is constructed based on wavelet method and the property of t distribution. However, the distribution of error sequence is always unknown. The computable confidence interval is obtained by the bootstrap method. The results of a simulation example show that the interval estimation based on approximate signal is superior to the interval estimation based on reconstructed signal in the sense of interval coverage probability, interval normalized averaged width and coverage width-based criterion.