Groeneboom's cube-root-log local limit conjecture for interval-censoring case 2

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 distribution function of $(T_i,U_i)$. Assume $0<F_0(t_0),H(t_0,t_0)<1$, and let $\hat F_n$ be the MLE of $F_0$. Groeneboom's local limit conjecture.

$$(n\log n)^{1/3}\frac{\hat F_n(t_0)-F_0(t_0)}{\{\frac34 f_0(t_0)^2/h(t_0,t_0)\}^{1/3}}\stackrel{{\cal D}}\longrightarrow 2Z,$$

where $Z$ is the last time that standard two-sided Brownian motion minus the parabola $y(t)=t^2$ reaches its maximum. This conjecture concerns the non-separated interval-censoring case, where observation intervals can be arbitrarily small.