Thinking the Unthinkable: Modern Non-Parametric Re-sampling Methods

Abstract

Classical parametric tests compare observed statistics to theoretical sampling distributions. Re-sampling is a revolutionary methodology because it departs from theoretical distributions; the inference is based upon repeated sampling within the same empirical sample. This definition encompasses Monte Carlo simulation, cross validation tests, jackknife and bootstrap procedures. The need for such methods is heightened by the vast amounts of data being collected in the modern information age, and by the increasingly complex scientific questions being asked. These factors have together led to the rapid development of modern non-parametric methods. An appealing feature of re-sampling methods is the way they combine an intuitive and layman-friendly applied aspect with challenging and elegant mathematics. Purpose of this review is to divulge the theoretical foundations of re-sampling and to facilitate a coherent use of this computational intensive research method.