Assuming that a sample estimator converges to some unknown constant (a wild assumption to be sure) and without assuming the distribution of either the sample estimator or the variables from which it was calculated, is there a general foolproof way to construct a confidence interval for that unknown constant?
Perusing some nonparametric statistics lectures online, the most widely described "general method" involves bootstrapping. On the other hand, bootstrapping doesn't work for some estimators e.g. estimating $\theta$ for $U(0, \theta)$, and the material on the conditions where bootstrapping works is hard to grasp for me. I've also come across subsampling, but while it's purportedly more widely applicable than bootstrapping and just as easy to code, I still don't understand when it's applicable anymore than I know for bootstrapping. It'd be great if more experienced people can point me in the right direction.