The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 2 (2014), 654-668.
Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band
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.
Ann. Statist. Volume 42, Number 2 (2014), 654-668.
First available in Project Euclid: 20 May 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G15: Tolerance and confidence regions
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Wang, Jiangyan; Liu, Rong; Cheng, Fuxia; Yang, Lijian. Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band. Ann. Statist. 42 (2014), no. 2, 654--668. doi:10.1214/13-AOS1197. https://projecteuclid.org/euclid.aos/1400592173
- Supplementary material: Supplement to “Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band”. This supplement contains additional technical proofs and some supporting numerical results.