Related papers: Statistical test for an urn model with random mult…
Different statistical samples (e.g., from different locations) offer populations and learning systems observations with distinct statistical properties. Samples under (1) 'Unconfounded' growth preserve systems' ability to determine the…
Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The Urn Model with…
For the plain Polya urn with two colors, black and white, we prove a functional central limit theorem for the number of white balls assuming that the initial number of black balls is large. Depending on the initial number of white balls,…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the…
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…
We consider a deposition model in which balls rain down at random towards a 2-dimensional surface, roll downwards over existing adsorbed balls, are adsorbed if they reach the surface, and discarded if not. We prove a spatial law of large…
This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and…
In this paper, we study two problems related to planar matchings in random bipartite graphs. First, we colour each edge of the complete bipartite graph $K_{n,n}$ uniformly randomly from amongst ${r}$ colours and show that if ${r}$ grows…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
This paper considers the $(n,k)$-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections $k$ at each step is on the same asymptotic order as the number…
We use the combinatorial properties of central sets to prove a result about the existence of exponential monochromatic patterns, in the style of Hindman's Finite Sums Theorem. More precisely, we prove that for every finite coloring of the…
We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…