Nonparametric bootstrapping for hierarchical data

Nonparametric bootstrapping for hierarchical data is relatively underdeveloped and not straightforward: certainly it does not make sense to use simple nonparametric resampling, which treats all observations as independent. We have provided some resampling strategies of hierarchical data, proved that the strategy of nonparametric bootstrapping on the highest level (randomly sampling all other levels without replacement within the highest level selected by randomly sampling the highest levels with replacement) is better than that on lower levels, analyzed real data and performed simulation studies.