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November 2017 Baxter’s inequality and sieve bootstrap for random fields
Marco Meyer, Carsten Jentsch, Jens-Peter Kreiss
Bernoulli 23(4B): 2988-3020 (November 2017). DOI: 10.3150/16-BEJ835


The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in $\mathbb{Z}^{2}$. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. 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.


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Marco Meyer. Carsten Jentsch. Jens-Peter Kreiss. "Baxter’s inequality and sieve bootstrap for random fields." Bernoulli 23 (4B) 2988 - 3020, November 2017.


Received: 1 June 2015; Revised: 1 February 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778277
MathSciNet: MR3654797
Digital Object Identifier: 10.3150/16-BEJ835

Keywords: Autoregression , bootstrap , Random fields

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 4B • November 2017
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