arXiv subjects

Songkiat Sumetkijakan

Publications and source records attributed to Songkiat Sumetkijakan.

6 recordsLinked to original sources

arXiv2026

SL-vine and $Δ$-vine copula models

Traditional multivariate copulas often fail to capture complex dependence structures and may impose restrictive assumptions that limit their applicability to real-world data. To address these issues, vine copulas provide a flexible framework by constructing multivariate models from bivariate copulas. The three main types are D-vines, C-vines and R-vines. To simplify computations, the simplifying assumption is often applied, assuming conditional copulas are independent of conditioning variables. This results in some variables exerting minimal influence on the conditional copulas. Therefore, this study explores two subclasses of R-vines with node degrees capped at three, assessing its performance against existing models. The statistical results demonstrate that the proposed degree-constrained vine structures can serve as effective alternatives to existing vine copula models.

stat.ME↗

arXiv2026

Tau-Rho Equality and Other Dependence Measures of a Subclass of Factorizable Copulas

Kendall's tau and Spearman's rho, two widely used dependence measures in statistics and risk management, are often treated as interchangeable, yet can disagree sharply: Schreyer et al.~(2017) established the exact region of attainable $(τ,ρ)$ pairs. We study the complementary question of equality, namely, identifying nontrivial families of copulas $C$ satisfying $τ_C=ρ_C$. We prove that this equality holds for every factorizable copula of the form $C_{e,α}\ast C_{β,e}$, where $α$ and $β$ are piecewise linear monotonic surjections (PLMS). For these PLMS-generated copulas, we study further dependence measures, including Chatterjee's rank correlation coefficient and tail dependence coefficients, revealing some useful algebraic formulas and unexpected phenomena. In particular, Chatterjee's coefficient can exhibit extreme asymmetry.

math.ST↗

arXiv2016

Supports of Implicit Dependence Copulas

A copula of continuous random variables $X$ and $Y$ is called an \emph{implicit dependence copula} if there exist functions $α$ and $β$ such that $α(X) = β(Y)$ almost surely, which is equivalent to $C$ being factorizable as the $*$-product of a left invertible copula and a right invertible copula. Every implicit dependence copula is supported on the graph of $f(x) = g(y)$ for some measure-preserving functions $f$ and $g$ but the converse is not true in general. We obtain a characterization of copulas with implicit dependence supports in terms of the non-atomicity of two newly defined associated $σ$-algebras. As an application, we give a broad sufficient condition under which a self-similar copula has an implicit dependence support. Under certain extra conditions, we explicitly compute the left invertible and right invertible factors of the self-similar copula.

math.ST↗

arXiv2012

Essential Closures and Supports of Multivariate Copulas

We generalize the notion of essential closures which is used in formulating a geometric necessary condition for a set to be the support of a multivariate copula. Furthermore, in some special cases, we derive an explicit formula of the support in terms of essential closures and obtain a stronger necessary condition.

math.ST↗

arXiv2012

On a Generalized $*$-Product for Copulas

This paper focuses on a generalization of the *-product called $\mathbf{C}$-product. This product, first introduced by Durante, Klement and Quesada-Molina, was used to characterize classes of compatible copulas. The $\mathbf{C}$-product of copulas $A$ and $B$ is defined to be an integral of a function which involves the copulas $A$ and $B$ and the family of copulas $\mathbf{C}$. However, measurability of the integrand in the definition is questionable. We will discuss this in details and attempt to re-define the product. Then we derive some properties of the re-defined product.

math.ST↗

arXiv2012

Shuffles of copulas and a new measure of dependence

Using a characterization of Mutual Complete Dependence copulas, we show that, with respect to the Sobolev norm, the MCD copulas can be approximated arbitrarily closed by shuffles of Min. This result is then used to obtain a characterization of generalized shuffles of copulas introduced by Durante, Sarkoci and Sempi in terms of MCD copulas and the $\star$-product discovered by Darsow, Nguyen and Olsen. Since shuffles of a copula is the copula of the corresponding shuffles of the two continuous random variables, we define a new norm which is invariant under shuffling. This norm gives rise to a new measure of dependence which shares many properties with the maximal correlation coefficient, the only measure of dependence that satisfies all of Rényi's postulates.

math.ST↗