Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation

DOI10.1214/aop/1176990943zbMath0705.62040OpenAlexW2058952802MaRDI QIDQ918079

Publication date: 1990

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176990943

zbMATH Keywords

product-limit estimator maximum likelihood estimators Kaplan-Meier estimator reproducing kernel Hilbert space uniform norm truncated data martingale representations strong approximations empirical process theory continuous distribution censored independent random variables compact LIL functional laws of iterated logarithm Glivenko-Cantelli like convergence martingale functional central limit theorems regularisations space of right continuous functions stochastic integral representations

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Strong limit theorems (60F15) Martingales with continuous parameter (60G44) Stochastic integrals (60H05) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

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