误差为线性AR过程回归模型HD估计的弱收敛速度

Rate of weak convergence of HD estimators in a regression model with linear AR process errors

考虑回归模型yt=xTtβ+et,t=1,2,…,n,其中误差et=atet-1+bt+ηt是平稳线性AR过程。讨论了该模型未知参数的Huber-Dutter估计的渐近性质,在合理的条件下,利用泰勒展开方法证明了估计量的弱收敛速度可以达到n-1[]2,同时还证明了误差过程et二阶矩的有界性,为更深入研究该模型大样本性质提供了基础。

Consider the following regression model yt=xTtβ+et(t=1,2,…,n)where the error et=atet-1+bt+ηt is a stationary AR process.In this paper the asymptotic behavior of Huber-Dutter estimators for unknown parameters in the above model is investigated.Under some regular conditions by the method of Taylor expansion the estimators weak converge to the true values with rate n-1[]2 is proved.And the boundedness of second moment of the error process is also proved.Then some foundational works have been finished for deeper study of large sample property in the above model.