M-ESTIMATORS OF LOCATION FOR GAUSSIAN AND RELATED PROCESSES WITH SLOWLY DECAYING SERIAL CORRELATIONS

• 成果类型: Article
• 署名作者: BERAN, J
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290401
• 发表日期: 1991
• 页码: 704-708
• 关键词: robustness

摘要

We investigate the behavior of M estimators of the location parameter for stochastic processes with long-range dependence. The processes considered are Gaussian or one-dimensional transformations of Gaussian processes. It turns out that, up to a constant, all M estimators are asymptotically equivalent to the arithmetic mean. For Gaussian processes this constant is always equal to one, independently of the psi-function. In view of the case of iid observations, the results are surprising. They are related to earlier work by Gastwirth and Rubin. Some simulations illustrate the results.