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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.23983 |
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| _version_ | 1866908995056304128 |
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| author | Milek, Janusz |
| author_facet | Milek, Janusz |
| contents | We study multivariate tail-dependence compatibility for complete and partial signed tail families, treating lower-tail, upper-tail, and mixed configurations in one geometric witness representation indexed by active coordinate sets and sign patterns. For a complete signed tail family, witness generator weights w = (w_{I,sigma}) give a linear incidence parametrization and are recovered by explicit triangular inversion. Excluding the geometric scale p0, the complete case uses 3^d - 1 generator weights, matching the number of complete signed tail coefficients; for partial specifications, only selected target coefficients need be prescribed. At a fixed threshold p0 in (0, 1/2), the inversion identifies the normalized noncentral ternary cell masses of any realizing copula. Hence finite-threshold compatibility is characterized by nonnegative recovered generator weights, singleton normalization, and the residual central-mass constraint.
This yields a complete Moebius-type synthesis within the witness framework. If the recovered increments are nonnegative and singleton normalization holds, then S(w) = sum(w) determines the admissible finite-scale range, and every admissible p0 gives an exact witness realization. In the canonical ray geometry, such a realization preserves the same complete signed tail family throughout 0 < p <= p0. Thus the primary object is the complete signed tail family lambda: it is realized at every admissible finite scale and can be carried along families of witness copulas with p0 decreasing to 0.
Partial, noisy, or inconsistent specifications are treated through linear-feasibility and weighted-l1 recovery problems in the same parametrization. The representation separates the p0-free incidence/Moebius layer from finite-threshold realization and provides tools for realization, simulation, calibration, completion, repair, and scenario design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23983 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Geometric Witness Framework for Signed Multivariate Tail-Dependence Compatibility: Asymptotic Structure and Finite-Threshold Synthesis Milek, Janusz Statistics Theory Probability Risk Management Methodology 60E05, 62H20, 90C05 We study multivariate tail-dependence compatibility for complete and partial signed tail families, treating lower-tail, upper-tail, and mixed configurations in one geometric witness representation indexed by active coordinate sets and sign patterns. For a complete signed tail family, witness generator weights w = (w_{I,sigma}) give a linear incidence parametrization and are recovered by explicit triangular inversion. Excluding the geometric scale p0, the complete case uses 3^d - 1 generator weights, matching the number of complete signed tail coefficients; for partial specifications, only selected target coefficients need be prescribed. At a fixed threshold p0 in (0, 1/2), the inversion identifies the normalized noncentral ternary cell masses of any realizing copula. Hence finite-threshold compatibility is characterized by nonnegative recovered generator weights, singleton normalization, and the residual central-mass constraint. This yields a complete Moebius-type synthesis within the witness framework. If the recovered increments are nonnegative and singleton normalization holds, then S(w) = sum(w) determines the admissible finite-scale range, and every admissible p0 gives an exact witness realization. In the canonical ray geometry, such a realization preserves the same complete signed tail family throughout 0 < p <= p0. Thus the primary object is the complete signed tail family lambda: it is realized at every admissible finite scale and can be carried along families of witness copulas with p0 decreasing to 0. Partial, noisy, or inconsistent specifications are treated through linear-feasibility and weighted-l1 recovery problems in the same parametrization. The representation separates the p0-free incidence/Moebius layer from finite-threshold realization and provides tools for realization, simulation, calibration, completion, repair, and scenario design. |
| title | A Geometric Witness Framework for Signed Multivariate Tail-Dependence Compatibility: Asymptotic Structure and Finite-Threshold Synthesis |
| topic | Statistics Theory Probability Risk Management Methodology 60E05, 62H20, 90C05 |
| url | https://arxiv.org/abs/2604.23983 |