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Entropy 2019, 21(2), 160;

A Comparison Study on Criteria to Select the Most Adequate Weighting Matrix

2,†,* and 3,*
CONICET-IELDE, National University of Salta, Salta A4408FVY, Argentina
Department of Economic Analysis, University of Zaragoza, 50005 Zaragoza, Spain
Department of Quantitative Methods, Law and Modern Languages, Technical University of Cartagena, 30201 Cartagena, Spain
Both authors contributed equally to this work.
Authors to whom correspondence should be addressed.
Received: 13 January 2019 / Revised: 6 February 2019 / Accepted: 6 February 2019 / Published: 8 February 2019
PDF [445 KB, uploaded 8 February 2019]


The practice of spatial econometrics revolves around a weighting matrix, which is often supplied by the user on previous knowledge. This is the so-called W issue. Probably, the aprioristic approach is not the best solution although, presently, there are few alternatives for the user. Our contribution focuses on the problem of selecting a W matrix from among a finite set of matrices, all of them considered appropriate for the case. We develop a new and simple method based on the entropy corresponding to the distribution of probability estimated for the data. Other alternatives, which are common in current applied work, are also reviewed. The paper includes a large study of Monte Carlo to calibrate the effectiveness of our approach compared to others. A well-known case study is also included.
Keywords: weights matrix; model selection; entropy; Monte Carlo weights matrix; model selection; entropy; Monte Carlo
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Herrera, M.; Mur, J.; Ruiz, M. A Comparison Study on Criteria to Select the Most Adequate Weighting Matrix. Entropy 2019, 21, 160.

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