Sequential Downscaling Methods for Estimation from Aggregate Data

Global change processes raise new estimation problems challenging the conventional statistical methods. These methods are based on the ability to obtain observations from unknown true probability distributions, whereas the new problems require recovering information from only partially observable or even unobservable variables. For instance, aggregate data exist at global and national level regarding agricultural production, occurrence of natural disasters, on incomes, etc. without providing any clue as to possibly alarming diversity of conditions at local level. “Downscaling” methods in this case should achieve plausible estimation of local implications emerging from global tendencies by using all available evidences. The aim of this paper is to develop a sequential downscaling method, which can be used in a variety of practical situations. Our main motivation for this was the estimation of spatially distributed crop production, i.e., on a regular grid, consistent with known national-level statistics and in accordance with geographical datasets and agronomic knowledge. We prove convergence of the method to a generalized cross-entropy maximizing solution. We also show that for specific cases this method is reduced to known procedures for estimating transportation flows and doubly stochastic matrices.