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Activity Number: 41
Type: Contributed
Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307559
Title: Smooth Simultaneous Confidence Bands for the Autoregressive Error Distribution Functions
Author(s): Jiangyan Wang*+ and Rong Liu and Fuxia Cheng and Lijian Yang
Companies: Soochow University and University of Toledo and Illinois State University and Michigan State University
Keywords: AR(p) ; bandwidth ; confidence band ; error ; kernel ; Kolmogorov distribution
Abstract:

We propose kernel estimator of the distribution function of the unobserved random errors in autoregressive time series. The estimator is based on the residuals computed by estimating the autoregressive coefficients with Yule-Walker method. Under mild assumptions, we establish oracle efficiency of the proposed estimator, i.e., it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. A smooth simultaneous confidence band is construct based on the proposed smooth distribution estimator and Kolmogorov distribution. Simulation examples support the asymptotic theory.


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