Abstract
Lately, there has been much discussion on the bootstrap resampling method, both as a way of estimating standard error and as a way of improving estimations with access to only one sample. However, little is found in literature discussing the size the bootstrap sample should take. This study aims to determine the existence of an optimum sampling fraction for resampling, analysing different estimators and number of resamples. An optimum fraction exists if, and only if, for every estimator and every amount of resamples, a fraction (or region) performs better in every population. Ten random populations were created by adding together different normal, Poisson and exponential distributions such that their means and variances are diverse. A Monte Carlo simulation with ten thousand iterations was done, taking random systematic samples from the populations and from these, bootstrap samples to estimate the mean, variance and respective standard errors. Results show the inexistence of a single optimum fraction. However, it does point to an optimum region for standard error estimation above 37.5%.
Highlights
Literature on bootstrap resampling is relatively plentiful, little is found on the size of the resample
The optimum sampling fraction is smaller than 100%, which means can we gain precision by restricting the sample, we get smaller computing costs for the same number of replications;
Based on the simulation studies made, we show the inexistence of a single optimum sampling fraction, which would be the best for every single estimation
Summary
Literature on bootstrap resampling is relatively plentiful, little is found on the size of the resample. These are optimum for some class though not all, for example the class of variance estimators or the class of standard errors estimators
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