长程相依情形下部分线性回归模型的估计理论

讨论固定设计点部分线性模型Yn,j=xn,jβ g（tn，j） En，jj=1，2，…；n，其中（xn,j,tn,j）∈R×0，1]是非随机的固定设计点，β是待估计的本知参数，g（.）是定义在0,1]则上的未知的光滑函数，{En,j}是长程相依的随机误差．本文在一定的正则性条件下得到了部分线性模型中参数β和函数g(.)的估计的弱相合性、均方相合性和收敛速度，同时得到了这些估计的渐近表示和渐近分布．本文所得到的结果与独立和弱相依情形下的结果有很大的差别．

Estimation Theory in Partly Linear Regression Models Under Long Range Dependence

Consistency, convergence rates, asymptotic representation and asymptotic distribation of the estimators of the patly linear regression setting are obtained when the random errors are either long range dependeni or a function of Gaussian random variables that are stationary and long range dependent. These represeatations are used to obtain the ltriting distribution and the convergence rates of the estimates. The results in this paper are drastically different from those encountered in the independent and weakly dependent cases.