UNIFORM MOMENT BOUNDS OF FISHER'S INFORMATION WITH APPLICATIONS TO TIME SERIES

• 成果类型: Article
• 署名作者: Chan, Ngai Hang; Ing, Chng-Kang
• 署名单位: Chinese University of Hong Kong; Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS861
• 发表日期: 2011
• 页码: 1526-1550
• 关键词: stochastic regression-models; AUTOREGRESSIVE PROCESSES; predictors; selection; identification; Consistency; principles; ORDER

摘要

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained. This asymptotic expression provides a solid theoretical foundation for some model selection criteria.