相关论文: Frank copula is minimum information copula under f…

We prove that Kendall's Rank correlation matrix converges to the Mar\v{c}enko-Pastur law, under the assumption that the observations are i.i.d random vectors $X_1$, $\dots$, $X_n$ with components that are independent and absolutely…

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…

Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the study of self-similar spaces, such as spaces with an expanding self-covering (e.g. Julia sets of complex rational functions). The dynamics of these…

Liouville's theorem, based on the Hamiltonian flow (micro-canonical ensemble) for a many particle system, indicates that the (stationary) equilibrium probability distribution is a function of the Hamiltonian. A canonical ensemble…

Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…

Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a…

An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann--Liouville type which is a…

Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…

In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…

In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities…

Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…

Machine learning models must continuously self-adjust themselves for novel data distribution in the open world. As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing…

This paper presents a method for fitting a copula-driven generalized linear mixed models. For added flexibility, the skew-normal copula is adopted for fitting. The correlation matrix of the skew-normal copula is used to capture the…

We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity…

We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate…

We study copula-based collective risk models when the dependence structure is defined by a Farlie-Gumbel-Morgenstern (FGM) copula. By leveraging a one-to-one correspondence between the class of FGM copulas and multivariate symmetric…

Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…