Estimates for the quantiles of smooth conditional distributions and the multidimensional invariance principle

DOI10.1007/BF02104663zbMath0881.60034MaRDI QIDQ1358017

Andrei Yu. Zaitsev

Publication date: 27 July 1997

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

multidimensional invariance principle

Mathematics Subject Classification ID

Foundations and philosophical topics in statistics (62A01) Functional limit theorems; invariance principles (60F17)

Related Items (3)

KMT coupling for random walk bridges ⋮ Multidimensional version of the results of Komlos, Major and Tusnady for vectors with finite exponential moments ⋮ The accuracy of strong Gaussian approximation for sums of independent random vectors

Cites Work

• A useful estimate in the multidimensional invariance principle
• On the Gaussian approximation of convolutions under multidimensional analogues of S. N. Bernstein's inequality conditions
• Strong invariance principles for partial sums of independent random vectors
• Extensions of results of Komlós, Major, and Tusnády to the multivariate case
• Approximation theorems for independent and weakly dependent random vectors
• THE KOMLÓS-MAJOR-TUSNÁDY APPROXIMATIONS AND THEIR APPLICATIONS
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• On the Rate of Convergence for the Invariance Principle
• On the Approximation of Convolutions by Normal Laws
• On large deviations
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