Related papers: Pseudo-binomial Approximation to $(k_1, k_2)$-runs
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…
We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…
Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics.…
In this article, we provide an extension of the Chen-Stein inequality for Poisson approximation in the total variation distance for sums of independent Bernoulli random variables in two ways. We prove that we can improve the rate of…
Correcting for skewness can result in more accurate tail probability approximations in the central limit theorem for sums of independent random variables. In this paper, we extend the theory to sums of local statistics of independent random…
The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…
The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional It\^o diffusion that almost surely converges to a weak solution of the given stochastic differential equation. Under suitable conditions, the…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…
The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in…
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…