Precision of systematic sampling and transitive methods

The use of the transitive methods for assessing the precision of systematic sampling is discussed. A key point of the transitive methods is the choice of a local model for the covariogram near the origin. The relationship between the regularity of the measurements and the regularity of their covariogram is given. This result is useful for choosing the appropriate covariogram model. A method for estimating the measurement regularity from discrete data is proposed for cases where it cannot be assessed a priori. Stereological. applications where sampling is based on geometric probes such as serial sections, point or line grids are also discussed. (C) 1999 Elsevier Science B.V. All rights reserved. AMS classifications: 62G05; 62G20; 62M30; 60D05.