ORACALLY EFFICIENT ESTIMATION OF AUTOREGRESSIVE ERROR DISTRIBUTION WITH SIMULTANEOUS CONFIDENCE BAND

• 成果类型: Article
• 署名作者: Wang, Jiangyan; Liu, Rung; Cheng, Fuxia; Yang, Lijian
• 署名单位: Soochow University - China; University System of Ohio; University of Toledo; Illinois State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1197
• 发表日期: 2014
• 页码: 654-668
• 关键词: nonparametric regression-models; bickel-rosenblatt test; time-series models; CONVERGENCE; density; tests

摘要

We propose kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the autoregressive coefficients with the Yule Walker method. Under mild assumptions, we establish oracle efficiency of the proposed estimator, that is, it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. Applying the result of Wang, Cheng and Yang [J. Nonparametr. Stat. 25 (2013) 395-407], the proposed estimator is also asymptotically indistinguishable from the empirical distribution function based on the unobserved errors. A smooth simultaneous confidence band (SCB) is then constructed based on the proposed smooth distribution estimator and Kolmogorov distribution. Simulation examples support the asymptotic theory.