The limit distribution of the concave majorant of an empirical distribution function

DOI10.1016/0167-7152(94)90238-0zbMath0801.62017OpenAlexW2054716539MaRDI QIDQ1332859

Yazhen Wang

Publication date: 5 September 1994

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(94)90238-0

zbMATH Keywords

Brownian motiongreatest convex minorantstrong approximationlimit distributionempirical distributionleast concave majorant

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Order statistics; empirical distribution functions (62G30)

Related Items (9)

The least concave majorant of the empirical distribution function ⋮ The distance between a naive cumulative estimator and its least concave majorant ⋮ The limit process of the difference between the empirical distribution function and its concave majorant ⋮ A general asymptotic scheme for inference under order restrictions ⋮ Distribution of global measures of deviation between the empirical distribution function and its concave majorant ⋮ A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation ⋮ Uniform central limit theorems for the Grenander estimator ⋮ Two-sided Brownian motion with quadratic drift and its least concave majorant ⋮ TheL₁theory of estimation of monotone and unimodal densities

Cites Work

• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Asymptotically minimax estimation of concave and convex distribution functions
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