Asymptotic expansion of M-estimators with long-memory errors

• 成果类型: Article
• 署名作者: Koul, HL; Surgailis, D
• 署名单位: Michigan State University; Vilnius University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1031833675
• 发表日期: 1997
• 页码: 818-850
• 关键词: range dependent errors; Empirical Process; models

摘要

This paper obtains a higher-order asymptotic expansion of a class of M-estimators of the one-sample location parameter when the errors form a long-memory moving average; A suitably standardized difference between an M-estimator and the sample mean is shown to have a limiting distribution. The nature of the limiting distribution depends on the range of the dependence parameter theta. If for example, 1/3 < theta < 1, then a suitably standardized difference between the sample median and the sample mean converges weakly to a normal distribution provided the common error distribution is symmetric. If 0 < theta < 1/3,then the corresponding limiting distribution is normal. This paper thus goes beyond that of Beran who observed, in the case of long-memory Gaussian errors, that M-estimators T-n of the one-sample location parameter are asymptotically equivalent to the sample mean in the sense that Var(T-n)/Var((X) over bar(n)) --> 1 and T-n = (X) over bar(n) + o(P)(root Var((X) over bar(n))).