Comparison of conventional, balanced and sufficient bootstrapping approaches via confidence intervals and efficiency

Abstract

There are various bootstrapping approaches depending on how bootstrap samples are selected. The conventional bootstrapping obtains random bootstrap samples by using all the units in the original sample. Balanced bootstrapping based on having individual observations with equal overall frequencies in all bootstrap samples and sufficient bootstrapping based on using only the distinct individual observations instead of all the units in the original sample are the two basic attempts proposed in this manner. This study compares the balanced, sufficient and conventional bootstrapping approaches in terms of efficiency, bootstrap confidence interval coverage accuracy, and average interval length. Although sufficient bootstrapping approach resulted in more efficient estimators and the narrower confidence intervals than the other two in all cases, none of the actual coverage level of confidence intervals was controlled within the desired limits. Conventional and balanced bootstrapping approaches have given quite similar results in terms of efficiency, coverage accuracy and average length.