  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.
