A shorter proof of Kanter's Bessel function concentration bound
Lutz Mattner,Bero Roos +1 more
TLDR
Barbour et al. as discussed by the authors gave a shorter proof of Kanter's (J. Multivariate Anal. 6, 222-236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors.Abstract:
We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I0(x) + I1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Cekanavicius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).read more
Citations
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Proceedings ArticleDOI
Learning Sums of Independent Integer Random Variables
TL;DR: In this article, it was shown that Θ(k, 1/e) is the minimum number of samples required to learn a poisson binomial distribution with high accuracy.
Journal ArticleDOI
Total variation error bounds for geometric approximation
TL;DR: In this paper, the authors develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest, which reduces the problem to the construction of a coupling between the original distribution and the discrete equilibrium distribution from renewal theory.
Journal ArticleDOI
Total variation error bounds for geometric approximation
TL;DR: In this article, a new formulation of Stein's method is developed to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest, which is based on the construction of a coupling between the original distribution and the discrete equilibrium distribution from renewal theory.
Journal ArticleDOI
Maximal probabilities of convolution powers of discrete uniform distributions
Lutz Mattner,Bero Roos +1 more
TL;DR: In this paper, the maximal probabilities of nth convolution powers of discrete uniform distributions were shown to be constant over root n upper bounds for the maximal probability of a discrete uniform distribution.
Journal ArticleDOI
On Negative Binomial Approximation
TL;DR: In this paper, negative binomial approximation to sums of independent Z +$-valued random variables using Stein's method is employed to obtain the error bounds Convolution of negative Binomial and Poisson distribution is used as a three-parametric approximation.
References
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TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
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