Variance Reduction Techniques for Monte Carlo Sampling from Student Distributions

A Monte Carlo design is presented for estimating the variance and cumulative distribution function of translation and scale invariant statistics based on independent Student random variables. One obvious application is studying estimates of the location parameter from a symmetric, possibly long-tailed distribution. The method itself amounts to suppressing some of the variability in the sampled objects by integrating these objects over appropriate regions of the underlying probability space. Indications are that, in cases of interest, the variability is thereby considerably reduced, as is illustrated in an application concerning trimmed and Winsorieed means.