Related papers: Martingale-Coboundary Representation for a Class o…
Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A special case of this result is that binomial tail…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
We examine the lattice generated by two pairs of supplementary vector subspaces of a finite-dimensional vector space by intersection and sum, with the aim of applying the results to the study of representations admitting two pairs of…
In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…
We establish an invariance principle for a general class of stationary random fields indexed by $\mathbb Z^d$, under Hannan's condition generalized to $\mathbb Z^d$. To do so we first establish a uniform integrability result for stationary…
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
This paper defines a linear representation for nonlinear maps $F:\mathbb{F}^n\rightarrow\mathbb{F}^n$ where $\mathbb{F}$ is a finite field, in terms of matrices over $\mathbb{F}$. This linear representation of the map $F$ associates a…
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and,…
For a fixed integer $k \ge 0$, consider representations of positive integers as sums of binomial coefficients of the form $\binom{n}{k}$. While exact minimal bounds for the number of required summands are known only in a few low-dimensional…