Distribution of global measures of deviation between the empirical distribution function and its concave majorant

DOI10.1007/s10959-007-0103-0zbMath1149.62039OpenAlexW2144853095MaRDI QIDQ927247

Vladimir N. Kulikov, Hendrik P. Lopuhaä

Publication date: 4 June 2008

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

Full work available at URL: https://doi.org/10.1007/s10959-007-0103-0

zbMATH Keywords

empirical processescentral limit theoremleast concave majorantBrownian motion with parabolic drift\(L_k\) distance

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30)

Related Items (8)

The distance between a naive cumulative estimator and its least concave majorant ⋮ The distribution of the maximal difference between a Brownian bridge and its concave majorant ⋮ Testing monotonicity of a hazard: asymptotic distribution theory ⋮ Limit theory in monotone function estimation ⋮ Efficient computation of the cdf of the maximal difference between a Brownian bridge and its concave majorant ⋮ Convergence of linear functionals of the Grenander estimator under misspecification ⋮ Refinements of the Kiefer-Wolfowitz theorem and a test of concavity ⋮ Testing equality of functions under monotonicity constraints

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