The Annals of Statistics

Universal Gaussian approximations under random censorship

Sándor Csörgő

Full-text: Open access

Abstract

Universal Gaussian approximations are established for empirical cumulative hazard and product-limit processes under random censorship. They hold uniformly up to some large order statistics in the sample, with the approximation rates depending on the order of these statistics, and require no assumptions on the censoring mechanism. Weak convergence results and laws of the iterated logarithm follow on the whole line if the respective processes are stopped at certain large order statistics, depending on the type of result. Some new consequences and negative results for confidence-band construction are discussed. Some new uniform consistency rates up to large order statistics are also derived and shown to be universally best possible for a wide range of tail order statistics.

Article information

Source
Ann. Statist., Volume 24, Number 6 (1996), 2744-2778.

Dates
First available in Project Euclid: 16 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032181178

Digital Object Identifier
doi:10.1214/aos/1032181178

Mathematical Reviews number (MathSciNet)
MR1425977

Zentralblatt MATH identifier
0868.62042

Subjects
Primary: 62G05: Estimation 62G30: Order statistics; empirical distribution functions
Secondary: 60F17: Functional limit theorems; invariance principles 60F15: Strong theorems

Keywords
Random censorship cumulative hazard product-limit Gaussian approximations

Citation

Csörgő, Sándor. Universal Gaussian approximations under random censorship. Ann. Statist. 24 (1996), no. 6, 2744--2778. doi:10.1214/aos/1032181178. https://projecteuclid.org/euclid.aos/1032181178


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