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Baxter`s inequality and sieve bootstrap for random fields

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  • Meyer, Marco
  • Jentsch, Carsten
  • Kreiss, Jens-Peter

Abstract

The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z2. 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.

Suggested Citation

  • Meyer, Marco & Jentsch, Carsten & Kreiss, Jens-Peter, 2015. "Baxter`s inequality and sieve bootstrap for random fields," Working Papers 15-06, University of Mannheim, Department of Economics.
  • Handle: RePEc:mnh:wpaper:38793
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    File URL: https://madoc.bib.uni-mannheim.de/38793/1/Meyer%2C_Jentsch%2C_Kreiss_15-06.pdf
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    References listed on IDEAS

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    1. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    2. Stephan Smeekes & Jean-Pierre Urbain, 2014. "On the Applicability of the Sieve Bootstrap in Time Series Panels," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 139-151, February.
    3. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
    4. Politis, D. N. & Romano, J. P., 1993. "Nonparametric Resampling for Homogeneous Strong Mixing Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 301-328, November.
    5. Jun Zhu & S. Lahiri, 2007. "Bootstrapping the Empirical Distribution Function of a Spatial Process," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 107-145, July.
    6. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
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    Cited by:

    1. Jentsch, Carsten & WeiƟ, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.

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    Keywords

    Autoregression ; bootstrap ; random fields;

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