Generalized bootstrap for estimators of minimizers of convex functions

Abstract

We introduce a generalized bootstrap technique for estimators obtained by minimizing functions that are convex in the parameter. We establish the consistency of these schemes via representation theorems. A number of classical resampling schemes, like the delete-d jackknife may be treated as special cases of this generalized bootstrap; and new ways of resampling are also introduced. Some of the schemes are computationally more efficient than classical techniques.