Indicator kriging estimator

The projection theory indicates that a projection estimator of the unknown I(2c z), such as a kriging estimator, is also a projection estimator (kriging) of its conditional expectation Fx(z (N)), (7) Consider then the indicator kriging estimator ... 

The indicator kriging estimator, I (x z), appears as a linear combination of the indicator data i(xa z), in the neighborhood, n," surrounding the point for which a prediction is to be made. This can be symbolized as ... 

Note that if the kriging weights Xi(z) are data values-independent, the indicator estimates (11) are not hence, the final estimate of the conditional cdf Fx(z (N)) is data values-dependent. For each cut-off Z], the kriging estimator (11) requires a different indicator covariance model ... 

The objective of indicator kriging is to estimate the local distribution of TCDD concentrations rather than the concentrations themselves. To apply indicator kriging, the data must be transformed from the original measurements of concentrations into indicator variables. This is accomplished by letting z(x ), a=l, N represent the initial data set... 

The goal of indicator kriging is to estimate the conditional distribution function of the unknown concentrations, Z(x) at... 

The cumulative distribution function at an unsampled location at threshold z can be estimated by krig-ing. This indicator kriging or IK requires a variogram measure of correlation corresponding to each threshold Zk, k=l,..., K. The IK process is repeated for all K threshold values that discretize the interval of variability of the continuous attribute Z. The distribution of uncertainty, built from assembling the K indicator krig-ing estimates, can be used for uncertainty assessment or simulation. 

The weights Xf(z) are cut-off z-dependent, and are determined as solutions of a linear system ( ) In fact, the indicator estimators used for the case-study underlying Figures 3 were obtained by a- slightly more elaborate technique called probability kriging or PK (9, 10) ... 

Geostatistical processing is one of the most useful and practical methods for evaluation and estimation of a resource. Its BLUE (Best Liner Unbiased Estimator) Kriging not only can indicate the distribution and amount of ore in a resource, but also, based on variance and error of Kriging can identify some parts of ore body, that have lack of data and need more exploration. For a routine Geostatistical processing some issues should be considered ... 

An estimate of the conditional distribution of Z(x) can be obtained by an ordinary kriging of the indicator transformed data. 

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