Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.16631

The relation between non-exchangeability and radial asymmetry of copulas

Damjana Kokol Bukovšek·Tomaž Košir·Blaž Mojškerc·Matjaž Omladič
View original source ↗Read source document ↗Export metadata ↓

Abstract

Non-exchangeability and radial asymmetry have got substantial attention in the literature, but relation between the two has not been studied yet. We propose the question: if a copula has a given degree of radial asymmetry, what is the range of possible values of the measure of non-exhangeability. We determine the set of all points whose first coordinate is the radial asymmetry of a copula and the second coordinate is its non-exchangeability. We show that this set is a non-convex hexagon.

Explore related subjects

math.STmath.PRstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Damjana Kokol Bukovšek, Tomaž Košir, Blaž Mojškerc, Matjaž Omladič. 2026-10-12. The relation between non-exchangeability and radial asymmetry of copulas. https://arxiv.org/abs/2610.16631

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Consistency of heritability estimation from summary statistics in high-dimensional linear models

In Genome-Wide Association Studies (GWAS), heritability is defined as the fraction of variance of an outcome explained by a large number of genetic predictors in a high-dimensional polygenic linear model. This work studies the asymptotic properties of the most common estimator of heritability from summary statistics called linkage disequilibrium score (LDSC) regression, together with a simpler and closely related estimator called GWAS heritability (GWASH). These estimators are analyzed in their basic versions and under various modifications used in practice including weighting and standardization. We show that, with some variations, two conditions which we call weak dependence (WD) and bounded-kurtosis effects (BKE) are sufficient for consistency of both the basic LDSC with fixed intercept and GWASH estimators, for both Gaussian and non-Gaussian predictors. For Gaussian predictors it is shown that these conditions are also necessary for consistency of GWASH (with truncation) and simulations suggest that necessity holds too when the predictors are non-Gaussian. We also show that, with properly truncated weights, weighting does not change the consistency results, but standardization of the predictors and outcome, as done in practice, introduces bias in both LDSC and GWASH if the two essential conditions are violated. Finally, we show that, when population stratification is present, all the estimators considered are biased, and the bias is not remedied by using the LDSC regression estimator with free intercept, as originally suggested by the authors of that estimator. These findings allow the user of the above estimates to evaluate whether they are useful for the data at hand.

math.ST↗
arXiv2026

Stein's unbiased risk estimate and Hyvärinen's score matching

Given a collection of observed signals corrupted with Gaussian noise, how can we learn to optimally denoise them? This fundamental problem arises in both empirical Bayes and generative modeling. In empirical Bayes, the predominant approach is via nonparametric maximum likelihood estimation (NPMLE), while in generative modeling, score matching (SM) methods have proven very successful. In our setting, Hyvärinen's implicit SM is equivalent to another classical idea from statistics---Stein's Unbiased Risk Estimate (SURE). Revisiting SURE minimization, we establish, for the first time, that SURE achieves nearly parametric rates of convergence of the regret in the classical empirical Bayes setting with homoscedastic noise. We also prove that SURE-training can achieve fast rates of convergence to the oracle denoiser in a commonly studied misspecified model. We show how to practically implement our method in settings involving heteroscedasticity and side-information, such as in an application to the estimation of economic mobility in the Opportunity Atlas. Our empirical results demonstrate the superior performance of SURE-training over NPMLE under misspecification. Collectively, our findings advance SURE/SM as a strong alternative to the NPMLE for empirical Bayes problems in both theory and practice.

math.ST↗
arXiv2026

An Operator-Theoretic Analysis of Nonlinear Filtering under Model Misspecification

We study nonlinear filtering with misspecified initial distributions and dynamics, but a correctly specified observation model. Observations are treated as a random process generated by the true model, rather than as fixed realizations, and both the correct filter and the misspecified filter are analyzed under this common observation law. Our main result is a Bayesian total variation balance identity for the expected change in total variation distance under a Bayesian update: a covariance term minus a non-negative remainder. The identity characterizes conditional and averaged update non-expansivity. Combined with prediction contraction, it yields finite-time bounds separating the initialization error from accumulated dynamical discrepancies, while allowing expansive updates. When the averaged updates are non-expansive and a uniform joint prediction--update coefficient is less than one, a persistent dynamical misspecification yields an asymptotic error bound proportional to the one-step discrepancy. When the conditional updates are non-expansive, we characterize an accumulated joint contraction that implies almost-sure and \(L^1\) coalescence of the true and misspecified filters. Finally, we verify update non-expansivity for scalar Gaussian predictive laws under a variance-ordering condition and, separately, derive explicit prediction contraction bounds for truncated kernels and bounded transition functions with elliptically symmetric noise.

math.ST↗