Fixed-design regression for linear time series

• 成果类型: Article
• 署名作者: Tran, L; Roussas, G; Yakowitz, S; Van, BT
• 署名单位: University of Arizona; University of California System; University of California Davis; Universite de Pau et des Pays de l'Adour
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 975-991
• 关键词: nonparametric function estimation; AUTOREGRESSIVE PROCESSES; dependent observations; Asymptotic Normality; mixing properties; models; errors

摘要

This investigation is concerned with recovering a regression function g(x(i)) on the basis of noisy observations taken at uniformly spaced design points x(i). It is presumed that the corresponding observations are corrupted by additive dependent noise, and that the noise is, in fact, induced by a general linear process in which the summand law can be discrete, as well as continuously distributed. Discreteness induces a complication because such noise is not known to be strong mixing, the postulate by which regression estimates are often shown to be asymptotically normal. In fact, as cited, there are processes of this character which have been proven not to be strong mixing. The main analytic result of this study is that, in general circumstances which include the non-strong mixing example, the smoothers we propose are asymptotically normal. Some motivation is offered, and a simple illustrative example calculation concludes this investigation. The innovative elements of this work, mainly, consist of encompassing models with discrete noise, important in practical applications, and in dispensing with mixing assumptions. The ensuing mathematical difficulties are overcome by sharpening standard arguments.