Estimators for the interval censoring problem

We study three estimators for the interval censoring case 2 problem, a histogram-type estimator, the maximum likelihood estimator (MLE) and the smoothed MLE, using a smoothing kernel. Our focus is on the asymptotic distribution of the estimators at a fixed point. The estimators are compared in a simulation study.

Estimating a concave distribution function from data corrupted with additive noise

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, ?). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational...

Current status data with competing risks: Consistency and rates of convergence of the MLE

We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Both types of estimators were studied by Jewell, van der Laan and Henneman [Biometrika ...

Current status data with competing risks: Limiting distribution of the MLE

We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 1031–1063] proved that both types of estimators converge globally...

Estimation of a convex function: Characterizations and asymptotic theory

We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case).We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of...