Estimating variances for all sample sizes by the bootstrap
A method is proposed for the simultaneous estimation of the variances of a sample statistic for all sample sizes using the bootstrap. It provides a potentially useful means for sample size determination based on a pilot sample when an explicit expression for the asymptotic variance is either too complex or unavailable at all. Since the bootstrap is employed, the method does not depend on any specific properties of the sample statistic and can therefore be universally implemented in a general computational algorithm. Although estimates of variances for all sample sizes are required, it is seen that bootstrap samples need only be generated for two selected sample sizes. It is shown that the resampling requirement to attain a given accuracy can be minimized by manipulating the two sample sizes for bootstrapping and the number of bootstrap samples allocated to each. While the variances of these bootstrap variance estimators can be made arbitrary small by increasing the number of bootstrap samples, it is also proved that the biases decrease rapidly to zero as the two sample sizes selected for bootstrapping increase.
bootstrap variance estimates sample size calculation intraclass correlation