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We describe a model-free, fully data-driven approach to simulating random draws from a continuous multivariate distribution. The proposed technique is an extension of the smoothed bootstrap which explicitly accounts for local differences in the dispersion of individual data points in the sample. Results from a number of simulation experiments suggest that in many cases, the procedure presented strikes a favourable balance between the conflicting objectives of adequately reflecting key characteristics of the underlying distributions and smoothing out the gaps between the individual data points in the sample...