Computation of general correlation coefficients for interval data

• Published in: International journal of approximate reasoning 2016-06, Vol.73, p.56-75
• Main Authors: Opara, Karol R., Hryniewicz, Olgierd
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; Computation; Correlation coefficients; Heuristic; Interval data; Intervals; Kendall's tau; Mathematical models; Measures of dependence; Optimization; Partial orders; Spearman's rho
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2016.02.007

This paper provides a comprehensive analysis of computational problems concerning calculation of general correlation coefficients for interval data. Exact algorithms solving this task have unacceptable computational complexity for larger samples, therefore we concentrate on computational problems arising in approximate algorithms. General correlation coefficients for interval data are also given by intervals. We derive bounds on their lower and upper endpoints. Moreover, we propose a set of heuristic solutions and optimization methods for approximate computation. Extensive simulation experiments show that the heuristics yield very good solutions for strong dependencies. In other cases, global optimization using evolutionary algorithm performs best. A real data example of autocorrelation of cloud cover data confirms the applicability of the approach. •Crisp and interval generalized correlation coefficients are discussed.•Outer bounds for Spearman's rho and Kendall's tau are derived.•Comparison of algorithms computing correlation coefficients for interval data.•Simple heuristic solutions prove effective for strong dependencies.•Simulation study and a real data example show applicability of the approach.