Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design

F. J. Alonso (), M. C. Bueso () and J. M. Angulo ()
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F. J. Alonso: University of Granada
M. C. Bueso: Technical University of Cartagena
J. M. Angulo: University of Granada

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 921-933

Abstract: Abstract Generalized statistical complexity measures provide a means to jointly quantify inner information and relative structural richness of a system described in terms of a probability model. As a natural divergence-based extension in this context, generalized relative complexity measures have been proposed for the local comparison of two given probability distributions. In this paper, the behavior of generalized relative complexity measures is studied for assessment of structural dependence in a random vector leading to a concept of ‘generalized mutual complexity’. A related optimality criterion for sampling network design, which provides an alternative to mutual information based methods in the complexity context, is formulated. Aspects related to practical implementation, and conceptual issues regarding the meaning and potential use of this approach, are discussed. Numerical examples are used for illustration.

Keywords: Generalized mutual information; Rényi entropy; Shannon entropy; Spatial sampling; Statistical complexity; 94A17; 62M30 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-016-9495-6

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