Related papers: Finite sample properties of the mean occupancy cou…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
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…
In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem…
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…
Let $X$ be a random variable with distribution function $F,$ and $X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P\{X_{i:n}\leq x\}.$ Using majorization…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for…
When using sampling-based motion planners, such as PRMs, in configuration spaces, it is difficult to determine how many samples are required for the PRM to find a solution consistently. This is relevant in Task and Motion Planning (TAMP),…
Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative error in S due to randomization. The bounds do not depend on the…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one…
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…
We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…