I am trying to estimate the following censored model: $y_{it}=\beta X_{it} + \epsilon_{it}$.
I only observe $y_{it}$ if $y_{it}\leq z_{it}$, otherwise $y_{it}=z_{it}$. The trick is that $z_{it}$ itself is random, and comes from some distribution $f\left(\cdot\right)$.
I think standard Tobit models do not apply since the threshold is random. Does this correspond to any standard model/application/package in R? Any non-parametric ideas are also welcome. Thanks!