On the consistency of the indirect lognormal correction

Abstract

The indirect lognormal correction is a change-of-support model commonly used in geostatistical applications when dealing with additive variables, for which the upscaling amounts to arithmetic averaging. It was designed as a generalization of the lognormal correction that states the permanence of lognormality, but so far its internal consistency has not been proven in the general case. After a recall of the theoretical conditions that change-of-support models must honor, the concept of conventional income is introduced and used to establish the mathematical consistency of the indirect lognormal correction. However, the suitability of this model is questionable in many situations, in particular when the support effect is important or when the point-support distribution presents a zero effect, is not continuous or not positively skewed.