The goal of this paper is to demonstrate that established rank correlation measures are not ideally suited for measuring rank correlation for numerical data that are perturbed by noise. We propose to use robust rank correlation measures based on fuzzy orderings. We demonstrate that the new measures overcome the robustness problems of existing rank correlation coefficients. As a first step, this...

Summary The ingenious approach of Chatterjee (2021) to estimate a measure dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This the appealing property being between 0 and 1, or 1 if only corresponding pair random variables is independent one measurable function other almost surely. However, more recent studies (Cao & Bickel 2020;...

introduction: teachers’ evaluation is one of the most important factors in decision making in university. it is done to determine the situation of  teaching activities. since the university rank in comprehensive exam of basic sciences(cebs) is indicated as educational success, this survey was carried out to determine the relationship between university ranks of  cebs in different courses and th...

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation matrix obtained from pairwis...

The property of synergy and its detection are discussed. A response surface is said to possess synergy if it is monotone in each argument and its level curves are convex. Detecting this property is particularly useful in the study of combination drug therapies where the goal is enhanced response or diminished side effect. One way to detect synergy is to fit a surface with linear level curves un...

This paper aims to demonstrate that established rank correlation measures are not ideally suited for measuring rank correlation for numerical data that are perturbed by noise. We propose a robust rank correlation measure on the basis of fuzzy orderings. The superiority of the new measure is demonstrated by means of illustrative examples.

We review both full-rank and reduced-rank parameterizations for correlation matrices. In particular, the full-rank parameterizations of Rebonato (1999d) and Schoenmakers and Coffey (2000), the reduced-rank angle parameterization of Rebonato (1999d) and Rebonato and Jäckel (1999), and the well known zeroed-eigenvalues reduced-rank approximation are described in detail. Numerical examples are pro...