WEAK-CONVERGENCE OF RANDOMLY WEIGHTED DEPENDENT RESIDUAL EMPIRICALS WITH APPLICATIONS TO AUTOREGRESSION

• 成果类型: Article
• 署名作者: KOUL, HL; OSSIANDER, M
• 署名单位: Oregon State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325383
• 发表日期: 1994
• 页码: 540-562
• 关键词: central limit-theorem; regression coefficients

摘要

This paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques. The weights need not be independent, bounded or even square integrable. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in pth-order autoregression models. The latter result, in turn, yields the asymptotic distributions of a class of robust and Jaeckel-type rank estimators. The main result is also used to obtain the asymptotic distributions of the least absolute deviation and certain other robust minimum distance estimators of the autoregression parameter vector.