The application of the jackknife in geostatistical resource estimation: Robust estimator and its measure of uncertainty.

Persistent Link:
http://hdl.handle.net/10150/186547
Title:
The application of the jackknife in geostatistical resource estimation: Robust estimator and its measure of uncertainty.
Author:
Adisoma, Gatut Suryoprapto
Issue Date:
1993
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The application of the jackknife in geostatistical resource estimation (in conjunction with kriging) is shown to yield two significant contributions. The first one is a robust new estimator, called jackknife kriging, which retains ordinary kriging's simplicity and global unbiasedness while at the same time reduces its local bias and oversmoothing tendency. The second contribution is the ability, through the jackknife standard deviation, to set a confidence limit for a reserve estimate of a general shape. Jackknifing the ordinary kriging estimate maximizes sample utilization, as well as information of sample spatial correlation. The jackknife kriging estimator handles the high grade smearing problem typical in ordinary kriging by assigning more weight to the closest sample(s). The result is a reduction in the local bias without sacrificing global unbiasedness. When data distribution is skewed, log transformation of the data prior to jackknifing is shown to improve the estimate by making the data behave better under jackknifing. The technique of block kriging short-cut, combined with jackknifing, are shown as an easy-to-use solution to the problem of grade estimation of a general three-dimensional digitized shape and the uncertainty associated with the estimate. The results are a single jackknife kriging estimate for the shape and its corresponding jackknife variance. This approach solves the problem of combining independent block estimation variances, and provides a simple way to set confidence levels for global estimates. Unlike the ordinary kriging variance, which is a measure of data configuration and is independent of data values, the jackknife kriging variance reflects the variability of the values being inferred, both on an individual block level and on the global level. Case studies involving two exhaustive (symmetric and highly skewed) data sets indicates the superiority of the jackknife kriging estimator over the original (ordinary kriging) estimator. Some instability of the log-transformed jackknife estimate is noted in the highly skewed situation, where the data do not generally behave well under standard jackknifing. A promising solution for future investigations seems to lie in the use of weighted jackknife formulation, which should better handle a wider spectrum of data distribution.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Kriging.; Geology -- Statistical methods.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mining and Geological Engineering; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Kim, Young C.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleThe application of the jackknife in geostatistical resource estimation: Robust estimator and its measure of uncertainty.en_US
dc.creatorAdisoma, Gatut Suryopraptoen_US
dc.contributor.authorAdisoma, Gatut Suryopraptoen_US
dc.date.issued1993en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe application of the jackknife in geostatistical resource estimation (in conjunction with kriging) is shown to yield two significant contributions. The first one is a robust new estimator, called jackknife kriging, which retains ordinary kriging's simplicity and global unbiasedness while at the same time reduces its local bias and oversmoothing tendency. The second contribution is the ability, through the jackknife standard deviation, to set a confidence limit for a reserve estimate of a general shape. Jackknifing the ordinary kriging estimate maximizes sample utilization, as well as information of sample spatial correlation. The jackknife kriging estimator handles the high grade smearing problem typical in ordinary kriging by assigning more weight to the closest sample(s). The result is a reduction in the local bias without sacrificing global unbiasedness. When data distribution is skewed, log transformation of the data prior to jackknifing is shown to improve the estimate by making the data behave better under jackknifing. The technique of block kriging short-cut, combined with jackknifing, are shown as an easy-to-use solution to the problem of grade estimation of a general three-dimensional digitized shape and the uncertainty associated with the estimate. The results are a single jackknife kriging estimate for the shape and its corresponding jackknife variance. This approach solves the problem of combining independent block estimation variances, and provides a simple way to set confidence levels for global estimates. Unlike the ordinary kriging variance, which is a measure of data configuration and is independent of data values, the jackknife kriging variance reflects the variability of the values being inferred, both on an individual block level and on the global level. Case studies involving two exhaustive (symmetric and highly skewed) data sets indicates the superiority of the jackknife kriging estimator over the original (ordinary kriging) estimator. Some instability of the log-transformed jackknife estimate is noted in the highly skewed situation, where the data do not generally behave well under standard jackknifing. A promising solution for future investigations seems to lie in the use of weighted jackknife formulation, which should better handle a wider spectrum of data distribution.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectKriging.en_US
dc.subjectGeology -- Statistical methods.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMining and Geological Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairKim, Young C.en_US
dc.contributor.committeememberHarpalani, Satyaen_US
dc.contributor.committeememberMyers, Donald E.en_US
dc.contributor.committeememberGlass, Charles E.en_US
dc.contributor.committeememberMcLaughlin, Carrolen_US
dc.identifier.proquest9421754en_US
dc.identifier.oclc703654307en_US
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