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We study the uniform convergence rate of the nonparametric maximum likelihoodestimator (MLE) for the sub-distribution functions in the current status datawith competing risks model. It is known that the MLE have $L^2$-normconvergence rate $O_P(n^{-1/3})$ in the absolutely continuous case, but thereis no arguments for the same rate of uniform convergence. We specify conditionsfor the uniform convergence rate $O_P(n^{-1/3}\log^{1/3} n)$ of the MLE for thesub-distribution functions of competing risks on finite intervals. The obtainedresult refines known uniform convergence rate in the particular case of currentstatus data. The main result is applied in order to get the uniform convergencerate of the MLE for the survival function of failure time in the current statusright-censored data model.

Uniform convergence rate of nonparametric maximum likelihood estimator for the current status data with competing risks