Translator Disclaimer
April 2014 Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band
Jiangyan Wang, Rong Liu, Fuxia Cheng, Lijian Yang
Ann. Statist. 42(2): 654-668 (April 2014). DOI: 10.1214/13-AOS1197

Abstract

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.

Citation

Download Citation

Jiangyan Wang. Rong Liu. Fuxia Cheng. Lijian Yang. "Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band." Ann. Statist. 42 (2) 654 - 668, April 2014. https://doi.org/10.1214/13-AOS1197

Information

Published: April 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1308.62096
MathSciNet: MR3210982
Digital Object Identifier: 10.1214/13-AOS1197

Subjects:
Primary: 62G15
Secondary: 62M10

Rights: Copyright © 2014 Institute of Mathematical Statistics

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.42 • No. 2 • April 2014
Back to Top