Speeding up bootstrap computations: a vectorized implementation for statistics based on sample moments

TL;DR

This paper introduces a vectorized method for non-parametric bootstrap computations based on sample moments, significantly improving speed by leveraging matrix operations, especially in languages like R.

Contribution

It presents a novel vectorized approach to bootstrap for sample moments, replacing resampling with weighted calculations for faster computation.

Findings

Significant speed improvements in bootstrap calculations.

Effective application to Pearson's correlation coefficient.

Applicable to matrix-oriented programming environments.

Abstract

In this note we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts, instead of evaluating the statistic on a re-sampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the gain in computational speed achieved by the vectorized implementation in real and simulated data sets, when bootstrapping Pearson's sample correlation coefficient.