统计研究 ›› 2008, Vol. 25 ›› Issue (11): 57-63.

• 论文 • 上一篇    下一篇

TAR模型加权秩估计及其性质讨论

耿修林 谢兆茹   

  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2008-11-15 发布日期:2008-11-15

Study on Randomly Weighted Rank Estimation About TAR(m, p, d) model

Geng Xiulin & Xie Zhaoru   

  • Received:1900-01-01 Revised:1900-01-01 Online:2008-11-15 Published:2008-11-15

摘要: 秩估计是上个世纪60年代逐渐兴起的一种非参数方法,由于它具有稳健性等特征,从而得到较为广泛的应用。本文主要讨论了TAR模型随机加权秩估计及其性质问题,证明了基于一般计分函数的线性秩统计量关于回归参数的渐近一致线性性。本文讨论的建立在计分规则基础上的秩估计方法,虽然以TAR模型为对象,但其基本原理同样可以应用到其他非线性模型的参数估计中。

关键词: TAR(m, p, d)模型, 秩估计, 渐近线性性

Abstract: Randomly weighted rank estimation based on a square-integrable, but not necessarily bounded, score function for the parameters in a kind of nonlinear time series(TAR) models are studied. The most important property, asymptotic uniform linearity(AUL), of a class of linear rank statistics in the TAR(p) models is derived. This AUL leads to the asymptotic normality of generalized rank estimators of regression parameters. The main idea in this paper also can be used to study generalized rank estimators for some other kinds of nonlinear time series models.


 

Key words: TAR(m, p, d) model, Rank estimates, Asymptotic linearity