Some stereological and statistical consequences derived from Cartier's formula
Christian Lantuéjoul · Journal of Microscopy · 1988
SUMMARY Let X and Y be two random variables with distribution functions Fx and FY, respectively. If Cartier's formula E[Y|X]=X holds, then Fx is necessarily less dispersed than FY. In this paper, the main consequences of Cartier's formula are derived. Some examples where such a formula holds are also given, namely in stereology (comparison of various estimators of Minkowsky's functionals) and in geostatistics (the change of support problem).