Abstract by Jared Clark
Exploring Alternatives to the Monte Carlo Bootstrap
Bootstrapping is a resampling technique that relies on taking random samples with replacement from a data set. These bootstrapping techniques provide researchers with an increased capacity to draw statistical inference from a sample. In order to approximate the bootstrap distribution of a statistic, Monte Carlo methods are the standard practice. In the case of statistics involving a summation (such as the mean) the Fourier Transform can be used, as an alternative, to provide estimates for the bootstrap distribution. The estimates generated using the Fourier Transform provide mathematical bounds for the actual bootstrap distribution as opposed to the stochastic bounds generated through Monte Carlo methods. If many Monte Carlo samples are desired, the Fast Fourier Transform can provide mathematical bounds that are narrower than the bounds of a Monte Carlo confidence interval in less time.