研究了带有一阶自回归误差结构的单指标模型的参数估计及其渐近性质问题, 利 用局部多项式回归的方法对未知的联系函数进行估计, 基于最大似然方法提出了模型的参数估计方法, 同时在一些基本的假设下证明了估计的相合性及其渐近正态性, 并给出模拟计算和应用实例以表明所提方法的有效性.

In this paper, the parametric estimation approaches and the asymptotics for a single-index model with the autoregressive processes of order one are investigated. First, the local polynomial regression method is used to estimate the unknown link function part. Second, a new estimation method based on maximum likelihood of the coefficients are given. Finally, the consistency and the asymptotic normality of the estimations are shown under mild assumptions. Moreover, some simulations and a real data example are given to show efficiency of our estimates.