Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
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Total variation between products of measures is at least a universal constant times that between the averaged measures' products.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
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Primitive Sequences for Probability Measures on Compact Intervals
Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
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A homogenization principle for total variation
Total variation between products of measures is at least a universal constant times that between the averaged measures' products.
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Scale selection for geometric medians on product manifolds
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.