m-Out-of-n Bootstrap

Abstract

Treated as a generalized version of the standard bootstrap, the m‐out‐of‐n bootstrap method is reviewed under three broad scenarios: (i) when the standard bootstrap works successfully, (ii) when the standard bootstrap is asymptotically correct but works poorly, and (iii) when the standard bootstrap fails. The last scenario, where the m‐out‐of‐n bootstrap provides an appealing remedy for the standard bootstrap, is covered in detail and illustrated with numerical examples. We also address briefly the issues of selection of m and uniform consistency.