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

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