Entropy-Based Solutions for Ecological Inference Problems: A Composite Estimator

Information-based estimation techniques are becoming more popular in the \ufb01eld of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The \ufb01rst one is the Generalized Maximum Entropy (GME) approach based on a matrix adjustment problem where the only observable information is given by the margins of the target matrix. An alternative approach is based on a distributionally weighted regression (DWR) equation. These two approaches have been studied so far as completely di\ufb00erent streams, even when there are clear connections between them. In this paper we present these connections explicitly. Morespeci\ufb01cally,weshowthatundercertainconditionsthegeneralizedcross-entropy(GCE)solution for a matrix adjustment problem and the GME estimator of a DWR equation di\ufb00er only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimatorthatcombinesthetwopriorsconsideredinbothapproaches. Finally,wepresentanumerical experiment and an empirical application based on Spanish data for the 2010 year