Two-sample hypothesis tests of means of a fuzzy random variable
Information Sciences: an International Journal - Fuzzy random variables
A similarity-based generalization of fuzzy orderings preserving the classical axioms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Fuzzy statistics: hypothesis testing
Soft Computing - A Fusion of Foundations, Methodologies and Applications
An introduction to ROC analysis
Pattern Recognition Letters - Special issue: ROC analysis in pattern recognition
The fuzzy approach to statistical analysis
Computational Statistics & Data Analysis
Information Sciences: an International Journal
The Gaussian rank correlation estimator: robustness properties
Statistics and Computing
A formal and empirical analysis of the fuzzy gamma rank correlation coefficient
Information Sciences: an International Journal
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Rank correlation measures are intended to measure to which extent there is a monotonic association between two observables. While they are mainly designed for ordinal data, they are not ideally suited for noisy numerical data. In order to better account for noisy data, a family of rank correlation measures has previously been introduced that replaces classical ordering relations by fuzzy relations with smooth transitions-thereby ensuring that the correlation measure is continuous with respect to the data. The given paper briefly repeats the basic concepts behind this family of rank correlation measures and investigates it from the viewpoint of robust statistics. Then, on this basis, we introduce a framework of novel rank correlation tests. An extensive experimental evaluation using a large number of simulated data sets is presented which demonstrates that the new tests indeed outperform the classical variants in terms of type II error rates without sacrificing good performance in terms of type I error rates. This is mainly due to the fact that the new tests are more robust to noise for small samples. The Gaussian rank correlation estimator turned out to be the best choice in situations where no prior knowledge is available about the data, whereas the new family of robust gamma test provides an advantage in situations where information about the noise distribution is available. An implementation of all robust rank correlation tests used in this paper is available as an R package from the CRAN repository.