Bounds on Spearman’s rho when at least one random variable is discrete
| Autor: | Pierre Zuyderhoff, Mhamed Mesfioui, Julien Trufin |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Economics and Econometrics 050208 finance 05 social sciences 01 natural sciences Upper and lower bounds 010104 statistics & probability Bounded function 0502 economics and business Statistics 0101 mathematics Statistics Probability and Uncertainty Random variable Mathematics |
| Zdroj: | European Actuarial Journal. 12:321-348 |
| ISSN: | 2190-9741 2190-9733 |
| Popis: | Spearman’s rho is one of the most popular dependence measures used in practice to describe the association between two random variables. However, in case of at least one random variable being discrete, Spearman’s correlations are often bounded and restricted to a sub-interval of $$[-1,1]$$ . Hence, small positive values of Spearman’s rho may actually support a strong positive dependence when getting close to its highest attainable value. Similarly, slight negative values of Spearman’s rho can actually mean a strong negative dependence. In this paper, we derive the best-possible upper and lower bounds for Spearman’s rho when at least one random variable is discrete. We illustrate the obtained lower and upper bounds in some situations of practical relevance. |
| Databáze: | OpenAIRE |
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