Tobias Fissler, Marc-Oliver Pohle
arXiv 7 Jul 2023 · Statistics — Methodology
arXiv:2307.03594 · PDF · DOI · OpenAlex · Extracted main text
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or thresholds. Deviations from these functionals are defined via generalised errors, often induced by identification or moment functions. As a normalised measure of dependence, a generalised correlation is constructed. Replacing the common Cauchy-Schwarz normalisation by a novel Fr\'echet-Hoeffding normalisation, we obtain attainability of the entire interval $[-1, 1]$ for any given marginals. We uncover favourable properties of these new dependence measures. The families of quantile and threshold correlations give rise to function-valued distributional correlations, exhibiting the entire dependence structure. They lead to tail correlations, which should arguably supersede the coefficients of tail dependence. Finally, we construct summary covariances (correlations), which arise as (normalised) weighted averages of distributional covariances. We retrieve Pearson covariance and Spearman correlation as special cases. The applicability and usefulness of our new dependence measures is illustrated on demographic data from the Panel Study of Income Dynamics.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | McNeil, A. J., Frey, R., and Embrechts, P (2015) Quantitative risk management: concepts, techniques and tools | 0.843 | 5 | 4 | 60% |
| 2 | Joe, H (2014) Dependence modeling with copulas | 0.843 | 3 | 3 | 100% |
| 3 | Mari, D. D. and Kotz, S (2001) Correlation and dependence | 0.843 | 3 | 3 | 100% |
| 4 | Embrechts, P., McNeil, A., and Straumann, D (2002) Correlation and dependence in risk management: properties and pitfalls | 0.830 | 7 | 3 | 57% |
| 5 | Balakrishnan, N. and Lai, C. D (2009) Continuous bivariate distributions | 0.737 | 3 | 2 | 100% |
| 6 | Coles, S., Heffernan, J., and Tawn, J (1999) Dependence measures for extreme value analyses | 0.737 | 3 | 2 | 100% |
| 7 | Lehmann, E. L (1966) Some concepts of dependence | 0.644 | 4 | 2 | 50% |
| 8 | Genest, C. and Neslehová, J (2007) A primer on copulas for count data | 0.644 | 2 | 2 | 100% |
| 9 | Stulp, G., Buunk, A. P., Pollet, T. V., Nettle, D., and Verhulst, S (2013) Are human mating preferences with respect to height reflected in actual pairings? | 0.585 | 3 | 1 | 100% |
| 10 | Blomqvist, N (1950) On a measure of dependence between two random variables | 0.511 | 2 | 1 | 100% |
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