Related papers: Characterisation of exchangeable sequences through…
We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…
Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a consequence, we can deduce discrepancy properties for the…
This research addresses the challenge of conducting interpretable causal inference between a binary treatment and its resulting outcome when not all confounders are known. Confounders are factors that have an influence on both the treatment…
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus…
It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…
The reciprocal Pascal matrix is the Hadamard inverse of the symmetric Pascal matrix. We show that the ordinary matrix inverse of the reciprocal Pascal matrix has integer elements. The proof uses two factorizations of the matrix of super…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
Recently it has been established that given an invertible frame multiplier with semi-normalized symbol, a specific dual of any of the two involved frames can be determined for the inversion purpose. The inverse can be represented as a…
Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisations for trading…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…
We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…