函数型核加权估计法及其在经济学中的应用

本文基于变系数模型提出了一个新的统计推断方法:函数型核函数加权最小二乘法.该方法将变系数模型中经典的核函数加权最小二乘法和参数模型中的函数型最小二乘法巧妙结合,通过条件特征函数构造损失函数进而定义了函数型核函数最小二乘估计量.该估计量既具有函数型最小二乘法的优势——在扰动项服从厚尾分布时也能够稳健估计参数,又具有非参数核估计的特点——估计量的相合性不依赖于参数模型的正确设定.同时,本文探讨了该估计量的大样本性质,证明了其相合性和渐近正态性.进一步,本文研究了该估计量的自适应估计,即基于估计量渐近方差的相合估计量来选择最优估计.最后,本文通过数值模拟来探究函数型核函数最小二乘法的有限样本性质,并将该方法应用到我国PM_(2.5)和经济增长关系的研究中.

Functional kernel-weighted least square estimation and its applications in economics

In this article, we propose a new method called functional kernel-weighted least squares (FKLS) method to estimate the smooth coefficient function in semi-parametric smooth coefficient model. This novel proposal ingeniously combines the kernel-weighted least squares (KLS) and the functional least squares (FLS) methods. The corresponding FKLS estimator is defined based on the loss function constructed by the conditional characteristic function. It not only has the advantage of FLS method that can produce robust parameter estimation even if the disturbance is subject to heavy tailed distributions, but also has the characteristics of non-parametric kernel estimation that consistency can be achieved without the knowledge of the correct functional form. The consistency and asymptotic normality of the proposed estimator are established. Furthermore, adaptive estimation is investigated based on the consistent estimator of the asymptotic variance. Finally, superiority of the FKLS estimator in finite samples, compared to the KLS estimator, is demonstrated through simulated numerical examples and the study of PM_2.5 and economic growth in China.