The limit process of the difference between the empirical distribution function and its concave majorant

DOI10.1016/j.spl.2006.04.026zbMath1106.60034OpenAlexW2101276010MaRDI QIDQ2432783

Vladimir N. Kulikov, Hendrik P. Lopuhaä

Publication date: 25 October 2006

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

Full work available at URL: https://doi.org/10.1016/j.spl.2006.04.026

zbMATH Keywords

empirical distribution functionleast concave majorantmonotone densityBrownian motion with parabolic driftisotonic estimation

Mathematics Subject Classification ID

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

Related Items (6)

The distance between a naive cumulative estimator and its least concave majorant ⋮ \(M\)-estimators for isotonic regression ⋮ Distribution of global measures of deviation between the empirical distribution function and its concave majorant ⋮ Limit theory in monotone function estimation ⋮ A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation ⋮ Improved inference for vaccine-induced immune responses via shape-constrained methods

Cites Work

• The limit distribution of the concave majorant of an empirical distribution function
• Asymptotic normality of the \(L_1\) error of the Grenander estimator
• On the distance between the empirical process and its concave majorant in a monotone regression framework. (Sur la distance entre le processus empirique et son majorant concave dans un modèle de régression monotone)
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Asymptotically minimax estimation of concave and convex distribution functions
• Convergence of stochastic processes

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