带有相依误差的函数型线性模型的复合分位数估计

Composite Quantile Regression for Functional Linear Models with Dependent Errors

本文研究了带有相依误差的函数型线性回归模型的复合分位数估计问题,其中误差来自短期相依和严平稳的线性过程.采用函数型主成分基函数对斜率函数和函数型预测变量进行展开并构造了斜率函数的估计,在相当宽松的条件下证明了斜率函数估计的最优收敛速度.最后通过理论模拟来评价所提出的方法,并给出了一个实际例子.

In this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.