Intentionally biased bootstrap methods

A class of weighted bootstrap techniques, called biased bootstrap or b-boot strap methods, is introduced. It is motivated by the need to adjust empiric al methods, such as the 'uniform' bootstrap, in a surgical way to alter som e of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduc e variance or to render some characteristic equal to a predetermined quanti ty. Examples of the last application include a b-bootstrap approach to hypo thesis testing in nonparametric contexts, where the b-bootstrap enables sim ulation 'under the null hypothesis', even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya-Watson kernel estimators to make them competitive with local linear smoothing. Ot her applications include density estimation under constraints, outlier trim ming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.