An optimal Berry-Esseen type theorem for integrals of smooth functions
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Publication:5742618
zbMath1423.60035arXiv1710.08503MaRDI QIDQ5742618
Publication date: 15 May 2019
Full work available at URL: https://arxiv.org/abs/1710.08503
penultimate approximationextreme point methodsapproximation by Rademacher averagesbinomial and normal approximationmoment and characteristic function inequalitiesosculatory inequalitiesZolotarev's \(\zeta\)-metrics
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- Some optimal bounds in the central limit theorem using zero biasing
- On the accuracy of the approximation of the complex exponent by the first terms of its Taylor expansion with applications
- On the extreme points of moments sets
- Probability in Banach spaces. Isoperimetry and processes
- A note on the normal approximation to the sum of independent random variables
- On the accuracy of the Gaussian approximation
- Stochastic orders
- Bounds on the constant in the mean central limit theorem
- Asymptotic expansions based on smooth functions in the central limit theorem
- Normal approximation - some recent advances
- A note on numerical rate of convergence estimates in central limit theorem
- On the rate of approximation in the central limit theorem
- Asymptotically proper constants in the Lyapunov theorem
- On the asymptotical behavior of the constant in the Berry-Esseen inequality
- On asymptotic expansion of the moments of smooth functions in the central limit theorem
- Closed form summation for classical distributions: variations on a theme of de Moivre
- On the accuracy of the normal approximation for sums of independent random variables
- On the accuracy of the normal approximation for sums of symmetric independent random variables
- What are cumulants?
- Cumulants are universal homomorphisms into Hausdorff groups
- On a functional contraction method
- An optimal Berry-Esseen type inequality for expectations of smooth functions
- A weak Cramér condition and application to Edgeworth expansions
- Zero bias transformation and asymptotic expansions
- Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
- Penultimate gamma approximation in the CLT for skewed distributions
- The Asymptotic Berry--Esseen Constant for Intervals
- Moment-Type Estimates with an Improved Structure for the Accuracy of the Normal Approximation to Distributions of Sums of Independent Symmetric Random Variables
- Nonimprovable Estimates for Asymptotic Expansions in the Central Limit Theorem
- A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorm. I.
- On the distance between convex-ordered random variables, with applications
- Normal Approximation and Asymptotic Expansions
- Parameterfreie Abschätzung und Realisierung von Erwartungswerten
- On the Normal Approximation to Symmetric Binomial Distributions
- Nonclassical Error Bounds for Asymptotic Expansions in the Central Limit Theorem
- On summation of independent variables in a non-classical situation
- An Improvement of the Lower Bound for the Rate of Convergence in Kolmogorov’s Uniform Limit Theorem
- A Non-Classical Error-Estimate in the Central Limit Theorem
- Extreme Points of Moment Sets
- On More Precise Convergence Rate Estimates in the Central Limit Theorem
- On the Convergence Rate in Kolmogorov’s Uniform Limit Theorem. I
- On the Convergence Rate in Kolmogorov’s Uniform Limit Theorem. II
- On the remainder in the central limit theorem
- A Non-Uniform Estimate for the Speed of Convergence in the Central Limit Theorem in R
- Asymptotic expansions in the central limit theorem under moment conditions
- The s-convex orders among real random variables, with applications
- Normal Approximation
- A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. II
- A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. III
- On Strengthening Lyapunov Type Estimates (The Case When the Distribution of the Summands is Close to the Normal Distribution)
- Real Analysis and Probability
- The Early History of the Cumulants and the Gram‐Charlier Series
- Telescoping Estimates for Smooth Series
- On the Asymptotically Exact Constants in the Berry–Esseen–Katz Inequality
- On the Convergence Rate in Lyapunov's Theorem
- A Moment Inequality with Application to Convergence Rate Estimates in the Global CLT for Poisson-Binomial Random Sums
- On Nonuniform Estimates of Approximation Exactness in the Central Limit Theorem
- On the Convergence of Moments in the Central Limit Theorem
- The General Moment Problem, A Geometric Approach
- On the Closeness of the Distributions of Two Sums of Independent Random Variables
- Extending n-convex functions
- The Extrema of the Expected Value of a Function of Independent Random Variables
- On minimal smoothness conditions for asymptotic expansions of moments in the CLT
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