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Nonparametric Resampling for Homogeneous Strong Mixing Random Fields

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  • Politis, D. N.
  • Romano, J. P.
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    Abstract

    Künsch (1989, Ann. Statist.17 1217-1241) and Liu ane Singh (1992, in Exploring Limits of Bootstrap (R. Le Page and L. Billard, Eds.), pp. 225-248, Wiley, New York) have recently introduced a block resampling method that is successful in deriving consistent bootstrap estimates of distribution and variance for the sample mean of a strong mixing sequence. Raïs and Moore (1990, in Interface '90) and Raïs (1992, Ph.D. Thesis, University of Montreal) extended the results of Künsch and Liu and Singh in the case of the sample mean of a homogeneous strong mixing random field in two dimensions (n = 2). In this paper, the general case (n [set membership, variant] Z+) is considered, and a resampling technique for strong mixing random fields is formulated, which is an extension of the "blocks of blocks" resampling scheme for sequences in Politis and Romano (1992, Ann. Statist.20 (4) 1985-2007). The "blocks of blocks" method can be used to construct asymptotically correct confidence intervals for parameters of the whole (infinite-dimensional) joint distribution of the random field, for example, the spectral density at a point. A variation of the "blocks of blocks" resampling scheme that involves "wrapping" the data around on a torus will also be studied, in view of its property to yield an unbiased bootstrap distribution.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 47 (1993)
    Issue (Month): 2 (November)
    Pages: 301-328

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    Handle: RePEc:eee:jmvana:v:47:y:1993:i:2:p:301-328

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    Cited by:
    1. Patrick Bajari & Jeremy T. Fox, 2005. "Measuring the Efficiency of an FCC Spectrum Auction," NBER Working Papers 11671, National Bureau of Economic Research, Inc.
    2. Buhlmann, Peter & Kunsch, Hans R., 1999. "Block length selection in the bootstrap for time series," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 295-310, September.
    3. Iranpanah, N. & Mohammadzadeh, M. & Taylor, C.C., 2011. "A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 578-587, January.
    4. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.

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