Abstract

This thesis presents an investigation into the estimator for the rate of convergence of a sequence of distribution functions given by Bertail, Politis and Romano (1999, Annals of Statistics ). The motivation behind the estimator is outlined in detail and subsequently a simulation is carried out in order to validate the results in the above paper. It is brought out through the simulation results that the constants involved in subsampling has to be chosen with care as subsample size affects the results wildly. In order to understand the disparity between the published results and our initial simulation results, the estimator was deconstructed and the results were reinterpreted. The basic reason for disparity is found in the fact that subsample sizes must be much smaller than the size of the sample from which the estimator is constructed, a fact not apparent in the original paper.