Bernardini Papalia Rosa, Fernandez Vazquez Esteban
Department of Statistical Sciences, University of Bologna, 40126 Bologna, Italy.
REGIOlab and Department of Applied Economics, University of Oviedo, 33003 Oviedo, Spain.
Entropy (Basel). 2020 Jul 17;22(7):781. doi: 10.3390/e22070781.
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.
基于信息的估计技术在生态推断领域正变得越来越流行。在这一估计技术分支中，可以指出两种替代方法。第一种是基于矩阵调整问题的广义最大熵（GME）方法，其中唯一可观测的信息由目标矩阵的边际给出。另一种替代方法基于分布加权回归（DWR）方程。到目前为止，这两种方法一直被作为完全不同的流派进行研究，即使它们之间存在明显的联系。在本文中，我们明确展示了这些联系。更具体地说，我们表明在某些条件下，矩阵调整问题的广义交叉熵（GCE）解和DWR方程的GME估计量仅在所考虑的先验信息方面有所不同。然后，我们更进一步，提出一种组合估计量，它结合了两种方法中所考虑的两个先验。最后，我们基于2010年西班牙的数据给出了一个数值实验和一个实证应用。
