Extrapolation of subsampling distribuition estimators: the iid and strong mixing cases

Politis & Romano (1994) proposed a general subsampling methodology for the construction of large-sample confidence regions for an arbitrary parameter under minimal conditions. Nevertheless, the subsampling distribution estimators may sometimes be inefficient (in the case of the sample mean of i.d.d. data, for instance) as compared to alternative estimators such as the bootstrap and/or the asymptotic normal distribution (with estimated variance). The authors investigate here the extent to which the performance of subsampling distribution estimators can be improved by interpolation and extrapolation techniques, while at the same time retaining the robustness property of consistent distribution estimation even in nonregular cases; both id.d. and weakly dependent (mixing) observations are considered.