On strong approximation of the multidimensional empirical process
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Publication:1232856
DOI10.1214/aop/1176995981zbMath0344.60022OpenAlexW2005249365MaRDI QIDQ1232856
Publication date: 1976
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1176995981
Multivariate distribution of statistics (62H10) Gaussian processes (60G15) Strong limit theorems (60F15)
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A note on strong approximations of multivariate empirical processes ⋮ Lower bounds on the approximation of the multivariate empirical process ⋮ A continuous form of post-stratification ⋮ Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields ⋮ Probabilities of maximal deviations for nonparametric regression function estimates ⋮ On quadratic functionals of the Brownian sheet and related processes ⋮ On the asymptotic distributions of weighted uniform mulitivariate empirical processes ⋮ A limit distribution of the square error deviation of nonparametric estimators of the regression function ⋮ A limit distribution of the square error deviation of nonparametric estimators of the regression function ⋮ The Haar-function construction of brownian motion indexed by sets ⋮ Empirical and Poisson processes on classes of sets or functions too large for central limit theorems ⋮ Invariance principles for sums of Banach space valued random elements and empirical processes ⋮ Weak and strong uniform consistency of kernel regression estimates
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