Tail behaviour for suprema of empirical processes

DOI10.1214/aop/1176992616zbMath0596.62053OpenAlexW2067103866WikidataQ105584332 ScholiaQ105584332MaRDI QIDQ1078954

Robert J. Adler, Lawrence D. Brown

Publication date: 1986

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176992616

zbMATH Keywords

Brownian sheetdistribution functiontail behaviourGaussian random fieldsmultivariate empirical processesempiricalupper and lower class resultscentered Gaussian processmultivariate Kolmogorov-Smirnov tests

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Exact distribution theory in statistics (62E15) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15) Large deviations (60F10)

Related Items (14)

Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives ⋮ Probability estimates for the distribution of Kolmogorov distance in the worst direction ⋮ Detecting change in a random sequence ⋮ A note on strong approximations of multivariate empirical processes ⋮ A note on supremum of a Kiefer process ⋮ Approximation of Kolmogorov–Smirnov test statistic ⋮ Tests and confidence bands for bivariate cumulative distribution functions ⋮ Increments and sample path properties of Gaussian processes ⋮ On the tight constant in the multivariate Dvoretzky-Kiefer-Wolfowitz inequality ⋮ On the errors committed by sequences of estimator functionals ⋮ Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices ⋮ On the asymptotic distributions of weighted uniform mulitivariate empirical processes ⋮ Independent block identification in multivariate time series ⋮ Probability tails of Gaussian extrema

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