Related papers: A note on Stein equation for weighted sums of inde…
The motivation of the note is to obtain a H\"{o}rmander-type $L^2$ estimate for $\bar\partial$ equation. The feature of the new estimate is that the constant is independent of the weight function. Moreover, our estimate can be used for…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.
In this short note, we obtain error estimates for Riemann sums of some singular functions.
We present an explicit formula for a weighted sum over the zeros of the Riemann zeta function. This weighted sum is evaluated in terms of a sum over the prime numbers, weighted with help of the Hermite polynomials. From the explicit formula…
We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…
For testing independence it is very popular to use either the $\chi^{2}$-statistic or $G^{2}$-statistics (mutual information). Asymptotically both are $\chi^{2}$-distributed so an obvious question is which of the two statistics that has a…
One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generator approach, one can solve for the solutions to the Stein…
In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…
Let $(X_{i}, i\in J)$ be a family of locally dependent nonnegative integer-valued random variables, and consider the sum $W=\sum\nolimits_{i\in J}X_i$. We first establish a general error upper bound for $d_{TV}(W, M)$ using Stein's method,…
Suppose $n$ independent random variables $X_1, X_2, \dots, X_n$ have zero mean and equal variance. We prove that if the average of $\chi^2$ distances between these variables and the normal distribution is bounded by a sufficiently small…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.
We obtain the estimate of difference between binomial and generalized binomial distributions in $\chi^2$ metric and in several other related metrics