一个有效估计:半参数非时齐扩散模型的局部线性复合分位回归估计

An Efficient Estimation:Local Linear Composite Quantle Regression for Semiparametric Time-Inhomogeneous Diffusion Models

主要研究半参数非时齐扩散模型的参数估计问题.基于非时齐扩散模型的离散观测样本,首先得到漂移参数的局部线性复合分位回归估计,并证明估计量的渐近偏差、渐近方差和渐近正态性.其次,讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,所得到的局部估计较局部线性最小二乘估计更为有效.最后,通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好.

The authors study the estimations of parameters for semiparametric time- inhomogeneous diffusion models. Based on discretely observed sample of time-inhomogeneous diffusion models, the local linear composite quantile regression （or CQR for short） estima- tions of the drift parameters are proposed, and the asymptotic bias, asymptotic variance and asymptotic normality of the local estimations are verified. The authors discuss the bandwidth selection and the asymptotic relative efficiency of the local linear CQR estima- tions comparing with the local linear least squares estimations, and it is shown that the proposed local estimations are much more efficient than the local linear least squares esti- mations. Furthermore, simulation results show that the proposed estimations have better performance than the local least squares estimations in diffusion models.