6 problems

Faster-rate conjecture. The nonparametric maximum likelihood estimator has a faster rate of convergence.

Let $F$ be an unknown distribution function on ${\mathbb R}^d$, with observations from the multivariate in-out interval-censoring model, and let $\hat{F}_n(\underline{t}_0)$ denote…

In the interval-censoring setting, let the NPMLE denote the nonparametric maximum likelihood estimator of the distribution function, and suppose that the NPMLE has $sqrt n$-converg…

Let $F_0$ and $H$ be continuously differentiable at $t_0$ and $(t_0,t_0)$, respectively, with strictly positive derivatives $f_0(t_0)$ and $h(t_0,t_0)$, where $H$ is the distributi…

In the case 2 interval-censoring model, let the unobservable event time be observed only through two inspection times, and let the MLE denote the maximum likelihood estimator of th…

Rate conjecture. The rate of the ordinary MLE should be improved from