The Bootstrap Small Sample Properties

This report reviews several bootstrap methods with special emphasis on small sample properties. Only those bootstrap methods are covered which promise wide applicability. The small sample properties can be investigated analytically only in parametric bootstrap applications. Thus there is a strong emphasis on the latter although the bootstrap methods can be applied nonparametrically as well. The disappointing confidence coverage behavior of several, computationally less extensive, parametric bootstrap methods should raise equal or even more concerns about the corresponding nonparametric bootstrap versions. The computationally more expensive double bootstrap methods hold great hope in the parametric case and may provide enough assurance for the nonparametric case.