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

Information-based estimation techniques are becoming more popular in the field of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The first 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 different streams, even when there are clear connections between them. In this paper we present these connections explicitly. More specifically, we show that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the GME estimator of a DWR equation differ only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimator that combines the two priors considered in both approaches. Finally, we present a numerical experiment and an empirical application based on Spanish data for the 2010 year.

Notes on Use of the Composite Estimator: an Improvement of the Ratio Estimator

This article discusses use of the composite estimator with the optimal weight to reduce the variance (or the mean-squared-error, MSE) of the ratio estimator. To study the practical usefulness of the proposed composite estimator, a Monte Carlo simulation is performed comparing the bias and MSE of composite estimators (with estimated optimal weight and with known optimal weight) with those of the simple expansion and the ratio estimators. Two examples, one regarding the estimation of dead fir trees via an aerial photo and the other regarding the estimation of the average sugarcane acres per county, are included to illustrate the use of the composite estimator developed here.