Some Approximation Problems in Statistics and Probability

DOI10.1007/978-3-642-36068-8_11zbMath1293.62037OpenAlexW92935565MaRDI QIDQ2848107

Yu. V. Prokhorov, Vladimir V. Ulyanov

Publication date: 25 September 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-36068-8_11

zbMATH Keywords

Hilbert spaceaccuracy of approximationspower divergence family of statisticseigenvalues of covariance operatorquadratic forms of random elementsshort asymptotic expansions

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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The Chebyshev--Edgeworth Correction in the Central Limit Theorem for Integer-Valued Independent Summands ⋮ Bounds for the chi-square approximation of the power divergence family of statistics ⋮ Asymptotic analysis of symmetric functions ⋮ A multivariate CLT for weighted sums with rate of convergence of order \(O(1/n)\) ⋮ Improved bounds in Stein's method for functions of multivariate normal random vectors ⋮ Explicit rates of approximation in the CLT for quadratic forms ⋮ On Bounds for Characteristic Functions of Powers of Asymptotically Normal Variables ⋮ High-dimensional central limit theorems by Stein's method ⋮ A precise local limit theorem for the multinomial distribution and some applications ⋮ On Properties of Polynomials in Random Elements ⋮ Bootstrap confidence sets for spectral projectors of sample covariance ⋮ Large ball probabilities, Gaussian comparison and anti-concentration

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