Applications of intentionally biased bootstrap methods

Abstract

A class of weighted-bootstrap techniques, called biased-bootstrap methods, is proposed. It is motivated by the need to adjust more conventional, uniform-bootstrap methods in a surgical way, so as to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the biased bootstrap can be used to reduce bias, or reduce variance, or render some characteristic equal to a predetermined quantity. More specifically, applications of bootstrap methods include hypothesis testing, variance stabilisation, both density estimation and nonparametric regression under constraints, 'robustification' of general statistical procedures, sensitivity analysis, generalised method of moments, shrinkage, and many more.