The accuracy of the Gaussian approximation to the sum of independent variates

By A. C. Berry. 1941

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Citations in the corpus

Adversarial Training and Robustness for Multiple Perturbations (2019, neutral): “[2] A.”
Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates (2018, methodology): “Similar to the proof of Theorem 1, we need to obtain a Berry-Esseen type bound for ŵ k −w∗ k. However, here, ŵ k is not a sample mean of n i.i.d. random variables, and thus we cannot directly apply the vanilla Berry-Esseen bound. Instead, we apply the following bound in Pinelis and Molzon (2016) on ”
Choosing between methods of combining p-values (2017, methodology): “For any particular combination method, the Berry—Esseen theorem (Berry, 1941) suggests the rate of convergence to normality depends on the so-called effective sample size implied by the weights, (∑n i=1 wi )2/∑n i=1 w2i .”
Probability distributions of bed load transport rates: A new derivation and comparison with field data (2010, methodology): “quantified with the Berry‐Esséen Theorem [Berry, 1941; Esséen, 1942], which states that the maximum difference between the real distribution and its normal approximation scales with N.”
A bound for the error in the normal approximation to the distribution of a sum of dependent random variables (1972, unknown): “77) IP{W _ a} (1)(a)I _ 3(R3 + |_ Iy dG(y) + zdH(z))-”
Privately Learning High-Dimensional Distributions (2018, methodology): “We apply the Berry-Esseen theorem Berry (1941); Esseen (1942); Shevtsova (2010) to approximate the distribution of Y by the standard normal distribution.”
An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums (2009, methodology): “for all nE1 and any F F 3 (Berry (1941), Esseen (1942)). The problem of establishing the best value of the constant C0 in inequality (1) is very important for the practical estimation of the accuracy of the normal approximation to the distributions of random variables which may be assumed to have th”
On the absolute constants in the Berry-Esseen-type inequalities (2011, background): “in (1) (see (Zolotarev, 1967a), (Zolotarev, 1967b)) turns out to be true, then, due to that β3 > 1, inequalities (3) and (4) will be sharper than the classical Berry–Esseen inequality (1) for β3 > 1.”
On Security Analysis of Proof-of-Elapsed-Time (PoET) (2017, methodology): “We will be using the central limit theorem and apply Berry–Esseen’s theorem [3,12] to bound the error of normal approximation:”
Fundamentals of Stein's method (2011, background): “1 Introduction The fundamental example of the type of result we will deal with in this article is the following version of the classical Berry-Esseen bound for the central limit theorem. Theorem 1.1. [13] Let X1,X2,... be i.i.d. random variables with E |X1|3 < ∞, [X1] = 0, andP Var(X1) = 1. If Φ ”
Variance-Gamma approximation via Stein's method (2013, background): “Berry-Esséen Theorem (Berry [6] and Esséen [16]) to hold; see Remark 4.”
IMPROVEMENT OF THE NON-UNIFORM VERSION OF BERRY-ESSEEN INEQUALITY VIA PADITZ-SIGANOV THEOREMS (2007, background): “Berry ([2]) and Carl-Gustav Esseen ([5]) in 1941 and 1945 respectively.”
A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis (2011, background): “’s FW (w) and Fn(w) and where Φn(t) may be seen as a function of some parameter n, is related to the Berry-Esseen upper bound (Berry, 1941; Esseen, 1945; Loève, 1977, Chap. VI, Sec. 21; Hwang, 1998), with ∆ ≥ max w∈S |FW (w)− Fn(w)|”
Statistical Approximating Distributions Under Differential Privacy (2018, methodology): “One approach is to use techniques like the Berry-Esseen theorem [Berry, 1941] or Stein’s method [Stein, 1972] to upper bound the rate of convergence of the sampling distribution of a statistic to its approximating distribution.”
An Analysis of the t-SNE Algorithm for Data Visualization (2018, background): “Lemma 3.8 (Berry-Esseen theorem (Berry, 1941; Esseen, 1942 , and Φ be the CDF of the standard normal distribution N (0 , 1) .”