Journal ArticleDOI
On the analytical structure of the constant in the nonuniform version of the esseen inequality
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In this paper, it was shown that for all neN and all xeR where c1 < 31.935, the analytical structure of C1=C1 is given without numerical calculation.Abstract:
Let X1,X2 be a sequence of independent random variable such that . It is shown that for all neN and all xeR where c1<31.935 In the general case only tha analytical structure of C1=C1 is given without numerical calculationread more
Citations
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Assessing interbank contagion using simulated networks
Grzegorz Hałaj,Christoffer Kok +1 more
TL;DR: A new approach to randomly generate interbank networks while overcoming shortcomings in the availability of bank-by-bank bilateral exposures is presented and a simplified measure—a so-called Systemic Probability Index—that also captures the likelihood of contagion from the failure of a given bank to honour its interbank payment obligations is proposed.
Stein's method for normal approximation
Louis H. Y. Chen,Qi-Man Shao +1 more
TL;DR: In this article, a general explanation of Stein's method as applied to the normal distribution is given, with the main emphasis on his approach exploiting an a priori estimate of the concentration function, and the use of concentration inequalities, in obtaining both uniform and non-uniform Berry-Esseen bounds for independent random variables.
Posted Content
Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria
TL;DR: In this paper, the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a representative finite sample was studied, and the authors derived exact finite sample solutions for experiments with normal, Bernoulli and bounded distributions of individual outcomes.
Journal ArticleDOI
Statistical treatment choice based on asymmetric minimax regret criteria
TL;DR: In this article, the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a finite sample is studied, where the regret is the expected welfare loss due to assigning inferior treatments.
Journal ArticleDOI
Gaussian Approximation for the Wireless Multi-Access Interference Distribution
TL;DR: A principled methodology is presented to establish rates of convergence of the multi-access interference distribution to a Gaussian distribution for general bounded and power-law decaying path-loss functions and a good statistical fit between the interference distribution and its Gaussian approximation is observed.
References
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Book
Sums of Independent Random Variables
TL;DR: In this paper, the authors define the notion of infinitely divisible distributions as the limits of the distributions of sums of independent random variables, and show that the distribution of a sum of independent non-identically distributed random variables converges to a given infinitely-divisible distribution.
Book
Normal Approximation and Asymptotic Expansions
Rabi Bhattacharya,R. Ranga Rao +1 more
TL;DR: In this paper, the Euler-MacLaurin sum formula for functions of several variables has been applied to the problem of convergence of probability measures and uniformity classes, and it has been shown that it is possible to obtain strong convergence for continuous, singular, and discrete probability measures.
Journal ArticleDOI
An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
Journal ArticleDOI
On the constant in the nonuniform version of the Berry-Esséen theorem
TL;DR: In this article, it was shown that for allnℕ∈ and allt∈ℝ, the Berry-Esseen Theorem holds for all n = 1.