Backtransforming Rank Order Kriging Estimates

Abstract

Kriging of raw data presenting distributions with positive skewness must be avoided because the strong influence of afew high values in the resulting estimates. The solution is to apply data transformation, which changes the shape of originaldistribution into a symmetric distribution. Kriging of transformed data is performed and then back-transformed to theoriginal scale of measurement. In this paper, we examine the uniform score transform that results in a uniform distribution.Ordinary kriging estimates of uniform score data results in a bell-shaped distribution, since the tails of the distribution arelost in the estimation process because of the smoothing effect. The back-transformation of this bell-shaped distributionresult in biased estimates. Therefore, the solution proposed in this paper is to correct the smoothing effect of the rank orderkriging estimates before transforming them back to the scale of raw data. Results showed this algorithm is reliable andback-transformed estimates are unbiased in relation to the sample data.

Keywords

• Data transformation
• Uniform score transformation
• Ordinary kriging
• Smoothing effect
• Back-transformation