Abstract
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.
Highlights
Ecological inference (EI) is the process of drawing conclusions about individual-level behavior from aggregate data, when no individual data are available
We have tackled the problem of providing reliable estimates of a target variable in a set of small geographical areas, by showing that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the Generalized Maximum Entropy (GME) estimator of a Distributionally Weighted Regression (DWR) equation differ only in terms of the a priori information considered
A composite estimator that combines the priors considered in both approaches is proposed and the performance among the three approaches is evaluated throughout Montecarlo experiments
Summary
Ecological inference (EI) is the process of drawing conclusions about individual-level behavior from aggregate (historically called “ecological”) data, when no individual data are available. We refer to the process of drawing conclusions about individual-level behavior from aggregate data, when no individual data are available or when individual data are incomplete In this inferential context, one problem is that many different possible relationships at the individual (or subgroup) level can generate the same observations at the aggregate (or group) level [8]. The information available for this inference exercise, together with the indicator yi· , is another disaggregated indicator xij that is related to the target indicator yij. This paper approaches this estimation problem in an attempt to unify two estimation strategies and it is organized as follows.
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