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Activity Number: 61 - New Developments in Complex Time Series Data
Type: Topic Contributed
Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract #324598
Title: Baxter's Inequality and Sieve Bootstrap for Random Fields
Author(s): Jens-Peter Kreiss* and Marco Meyer and Carsten Jentsch
Companies: TU Braunschweig and TU Braunschweig and University of Mannheim
Keywords: Bootstrap ; Autoregression ; Random Fields ; Baxter inequality

The concept of the autoregressive sieve bootstrap is investigated for the case of spatial processes. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates. The paper explores the range of validity of this resampling procedure and provides a general check criterion, which allows to decide whether the AR sieve bootstrap asymptotically works for a specific statistic of interest or not. The criterion may be applied to a large class of stationary spatial processes. As another major contribution of this paper, a weighted Baxter-inequality for spatial processes is provided. This result yields a rate of convergence for the finite predictor coefficients, i.e. the coefficients of finite-order AR model fits, towards the autoregressive coefficients, which are inherent to the underlying process under mild conditions. The developed check criterion is applied to some particularly interesting statistics like sample autocorrelations and standardized sample variograms. A simulation study shows that the procedure performs very well compared to normal approximations as well as block bootstrap methods in finite samples.

Authors who are presenting talks have a * after their name.

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