Pamukkale University Journal of Engineering Sciences (Feb 2020)
An empirical look at the variation associated with bootstrap estimates of location parameters
Abstract
Bootstrap is a technique for estimating standard error and bias of the statistic of interest. The idea behind the bootstrap technique is that bootstrap distribution generated by resampling from the sample at hand mimics the sampling distribution of the statistic. Nevertheless, the effect of sample size and number of bootstrap replications on the accuracy of bootstrap predictions is rarely considered and ignored while applying bootstrap. Although there exist limited studies on this matter in the literature, results obtained in these studies are expressed based on the population distribution. In this paper, we provide results of an empirical study that examines the relationship between sample size and number of bootstrap replications and standard errors of bootstrap estimates of location parameters for different population distributions. To that end, we focus on the representativeness of bootstrap distribution to sampling distribution for different continuous and discrete population distributions and different sample sizes, firstly. According to application results, we observe that sample size has more impact on accuracies of bootstrap estimates as regards to number of bootstrap replications. Additionally, we confirm that bootstrap distributions of median based on small sample sizes are inadequate for representing sampling distribution. Lastly, in order to model relationship between standard errors of bootstrap estimates and sample size and number of bootstrap estimations independently of population distribution, we propose a methodology based on jackknife-after-bootstrap technique and regression modeling.
