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Robust Resampling Confidence Intervals for Empirical Variograms

Journal Article


Abstract


  • The variogram function is an important measure of the spatial dependencies

    of a geostatistical or other spatial dataset. It plays a central role in kriging, designing

    spatial studies, and in understanding the spatial properties of geological and

    environmental phenomena. It is therefore important to understand the variability attached

    to estimates of the variogram. Existing methods for constructing confidence

    intervals around the empirical variogram either rely on strong assumptions, such as

    normality or known variogram function, or are based on resampling blocks and subject

    to edge effect biases. This paper proposes two new procedures for addressing

    these concerns: a quasi-block-bootstrap and a quasi-block-jackknife. The new methods

    are based on transforming the data to decorrelate it based on a fitted variogram

    model, resampling blocks from the decorrelated data, and then recorrelating. The

    coverage properties of the new confidence intervals are compared by simulation to a

    number of existing resampling-based intervals. The proposed quasi-block-jackknife

    confidence interval is found to have the best properties of all of the methods considered

    across a range of scenarios, including normally and lognormally distributed data

    and misspecification of the variogram function used to decorrelate the data.

Publication Date


  • 2011

Citation


  • Clark, R. Graham. & Allingham, S. F. (2011). Robust Resampling Confidence Intervals for Empirical Variograms. Mathematical Geosciences, 43 (2), 243-259.

Scopus Eid


  • 2-s2.0-78751664765

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1493

Has Global Citation Frequency


Number Of Pages


  • 16

Start Page


  • 243

End Page


  • 259

Volume


  • 43

Issue


  • 2

Abstract


  • The variogram function is an important measure of the spatial dependencies

    of a geostatistical or other spatial dataset. It plays a central role in kriging, designing

    spatial studies, and in understanding the spatial properties of geological and

    environmental phenomena. It is therefore important to understand the variability attached

    to estimates of the variogram. Existing methods for constructing confidence

    intervals around the empirical variogram either rely on strong assumptions, such as

    normality or known variogram function, or are based on resampling blocks and subject

    to edge effect biases. This paper proposes two new procedures for addressing

    these concerns: a quasi-block-bootstrap and a quasi-block-jackknife. The new methods

    are based on transforming the data to decorrelate it based on a fitted variogram

    model, resampling blocks from the decorrelated data, and then recorrelating. The

    coverage properties of the new confidence intervals are compared by simulation to a

    number of existing resampling-based intervals. The proposed quasi-block-jackknife

    confidence interval is found to have the best properties of all of the methods considered

    across a range of scenarios, including normally and lognormally distributed data

    and misspecification of the variogram function used to decorrelate the data.

Publication Date


  • 2011

Citation


  • Clark, R. Graham. & Allingham, S. F. (2011). Robust Resampling Confidence Intervals for Empirical Variograms. Mathematical Geosciences, 43 (2), 243-259.

Scopus Eid


  • 2-s2.0-78751664765

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1493

Has Global Citation Frequency


Number Of Pages


  • 16

Start Page


  • 243

End Page


  • 259

Volume


  • 43

Issue


  • 2