Development of the kriging method with application.
type: Item
instance of: scholarly article
title: Development of the kriging method with application.
zbMATH Open document ID: 1091.62097
DOI: 10.1023/A:1021793304115
author: Pavel Krejčíř
published in: Applications of Mathematics
publication date: 2005-07-01T00:00:00Z
full work available at URL: https://eudml.org/doc/33114
review text: The real airborne data on the environmental gamma radioactivity in two areas of United Kingdom inspired this paper summarizing a part of the author's PhD Thesis. The considered problem is to estimate the total radioactivity inventory on the examined area, i.e., the definite integral of a non-stationary random function \(Z(s)\) from its values in locations \(s_i,\;i=1,\dots , n.\) The procedure of the optimal linear prediction, known as universal kriging, was modified and used for the considered data. Because of its complexity (unknown non-constant trend \(\Lambda (s)\), different mean values in particular subareas, etc.), the data had to be first suitably stabilized; the best results have been obtained by the square-root transformation \(Y(s_i)=\sqrt {Z(s_i)}\) and then the kriging method was applied under the assumption that the residual random process \(U(s)=Y(s)-\Lambda (s)\) is a Gaussian second order stationary spatial process. The obtained results were compared with two simple estimates of the total inventory (based on the regridding method consisting in the recalculation of the data to a regular lattice and on the observed mean value of the radioactivity) and gave comparable values. However, only the kriging method provides an estimator of the confidence interval for the prediction.
reviewed by: Ivan Saxl
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 62P12
Mathematics Subject Classification ID: 62M20
zbMATH DE Number: 2185179
zbMATH Keywords: stochastic spatial process
zbMATH Keywords: second order stationarity
zbMATH Keywords: kriging
zbMATH Keywords: prediction
MaRDI profile type: Publication
cites work: Model-Based Geostatistics
cites work: Approximation Theorems of Mathematical Statistics
cites work: Predicting integrals of random fields using observations on a lattice
OpenAlex ID: W2100973989
description: scientific article; zbMATH DE number 2185179