Related papers: On the expected number of different records in a r…
The Birnbaum-Saunders distribution has been widely applied in several areas of science and although several methodologies related to this distribution have been proposed, the problem of determining the optimal sample size for estimating its…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…
The size distribution of aerosol droplets is a key parameter in a myriad of processes, and it is typically measured with optical aids (e.g., lasers or cameras) that require sophisticated calibration, thus making the measurement cost…
We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for…
We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the…
Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…
Rejection sampling is a popular method used to generate numbers that follow some given distribution. We study the use of this method to generate random numbers in the unit interval from increasing probability density functions. We focus on…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
We study the amount of information that is contained in "random pictures", by which we mean the sample sets of a Boolean model. To quantify the notion "amount of information", two closely connected questions are investigated: on the one…
Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…
In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular…
We investigate the high-probability estimation of discrete distributions from an \iid sample under $\chi^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely…