Poincaré inequalities and normal approximation for weighted sums

DOI10.1214/20-EJP549zbMath1473.60042arXiv2011.09237OpenAlexW3117705332MaRDI QIDQ2042650

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

Publication date: 21 July 2021

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.09237

zbMATH Keywords

central limit theoremnormal approximationtypical distributions

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05)

Related Items (2)

Inference via randomized test statistics ⋮ Limit theorems for the volumes of small codimensional random sections of \(\ell_{p}^{n}\)-balls

Cites Work

• Normal approximation for weighted sums under a second-order correlation condition
• A Berry-Esseen type inequality for convex bodies with an unconditional basis
• Power-law estimates for the central limit theorem for convex sets
• Gaussian marginals of convex bodies with symmetries
• Berry-Esseen bounds for projections of coordinate symmetric random vectors
• On concentration of distributions of random weighted sums
• Moment estimates derived from Poincaré and logarithmic Sobolev inequalities
• Berry-Esseen bounds for typical weighted sums
• Gaussian mixtures and normal approximation for V. N. Sudakov's typical distributions
• Thin shell implies spectral gap up to polylog via a stochastic localization scheme
• Pointwise estimates for marginals of convex bodies
• On a theorem of V. N. Sudakov on typical distributions
• A central limit theorem for convex sets
• The central limit problem for random vectors with symmetries
• Stability Problems in Cramér-Type Characterization in case of I.I.D. Summands
• Proximity of probability distributions in terms of Fourier-Stieltjes transforms
• On Talagrand's deviation inequalities for product measures
• A Topological Application of the Isoperimetric Inequality
• The central limit problem for convex bodies
• Variations on the Berry--Esseen Theorem
• Edgeworth Corrections in Randomized Central Limit Theorems
• Remarks on the Central Limit Theorem for Non-convex Bodies
• Second-order concentration on the sphere
• Tail-Sensitive Gaussian Asymptotics for Marginals of Concentrated Measures in High Dimension
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Poincaré inequalities and normal approximation for weighted sums