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Limit theorems for a general weighted process under random censoring
Author(s) -
Einmahl John H.J.,
Koning Alex J.
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315576
Subject(s) - mathematics , law of the iterated logarithm , martingale (probability theory) , central limit theorem , censoring (clinical trials) , logarithm , random variable , iterated function , iterated logarithm , convergence of random variables , limit (mathematics) , law of large numbers , discrete mathematics , statistics , mathematical analysis
Necessary and sufficient conditions for weak and strong convergence are derived for the weighted version of a general process under random censoring. To be more explicit, this means that for this process complete analogues are obtained of the Chibisov‐O'Reilly theorem, the Lai‐Wellner Glivenko‐Cantelli theorem, and the James law of the iterated logarithm for the empirical process. The process contains as special cases the so‐called basic martingale, the empirical cumulative hazard process, and the product‐limit process. As a tool we derive a Kiefer‐process‐type approximation of our process, which may be of independent interest.