The authors study the maximum likelihood estimators , of E. L. Kaplan and P. Meier [J. Am. Stat. Assoc. 53, 457-481 (1958; Zbl 0089.148)], for a continuous distribution function F onto R, on censored independent random variables, and those for of D. Lynden-Bell [Mon. Not. R. Astron. Soc. 155, 95-118 (1971)], J. C. Jackson [ibid. 166, 281-295 (1974)], and M. Woodroofe [Ann. Stat. 13, 163-177 (1985; Zbl 0574.62040)], on truncated data, and their regularisations near the boundary of the support supp(dF).
The theorems develop ideas of R. Gill [ibid. 11, 49-58 (1983; Zbl 0518.62039)] and give the compact LIL and the Glivenko-Cantelli like convergence with a power rate for these estimators in the space of right continuous functions D(supp(dF)), endowed with the uniform norm. The proofs are based on known martingale representations and martingale functional CLTs for , .