Strong limit theorems for osciallation moduli of PL-process and cumulative hazard process under truncation and censorship with applications
type: Item
instance of: scholarly article
title: Strong limit theorems for osciallation moduli of PL-process and cumulative hazard process under truncation and censorship with applications
zbMATH Open document ID: 0947.62033
DOI: 10.1007/BF02650667
author: Yong Zhou
author: Liuquan Sun
publication date: 2000-10-19T00:00:00Z
review text: Let \(F_n\) be the product-limit estimator of the survival distribution \(F\) for left truncated and right censored data. Define the PL-process as \[ \alpha_n(x)=\sqrt{n}\left(F_n(x)-F(x)\right), \] the oscillation moduli of \(\alpha_n\) as \[ \omega_n(a_n)=\sup\left\{\left|\alpha_n(t)-\alpha_n(s)\right|: |t-s|\leq a_n\right\}, \] and the Lipschitz-\(2^{-1}\) moduli of \(\alpha_n\) as \[ \tilde\omega_n(a_n)=\sup\left\{\left|\alpha_n(t+h)-\alpha_n(t)\right|h^{-1/2} : h\geq a_n\right\}, \] where \((a_n,n\geq 1)\) is a positive sequence. Strong limit theorems for \(\omega_n(a_n)\) and \(\tilde\omega_n(a_n)\) are given. Similar results for the standard estimator of the cumulative hazard function are presented.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 1321989
zbMATH Keywords: truncation
zbMATH Keywords: oscillation modulus
zbMATH Keywords: PL-processes
zbMATH Keywords: cumulative hazard process
zbMATH Keywords: censorship
reviewed by: Ryszard Zieliński
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02650667
OpenAlex ID: W2086367968
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 1321989