For any estimator obtained by solving , a generalized bootstrap technique is
introduced. This is a suitable generalization of the paired bootstrap, delete-
jackknives (for any ), Bayesian bootstrap, -out-of- bootstrap, and several other
variations of the bootstrap. Consistency and higher order accuracy results for
the generalized bootstrap is obtained. We also discuss how to extend the
proposed method for -functionals of the data, examples of which are
multivariate medians, data depth measures and so on. In some instances the
generalized bootstrap offers algorithms with remarkable computational advantage
over classical techniques.