Bootstrap Methods: Another Look at the Jackknife

We discuss the following problem: given a random sample \mathbf{X} = (X_1, X_2, \cdots, X_n)from an unknown probability distribution F estimate the sampling distribution of some prespecified random variable R(\mathbf{X}, F) on the basis of the observed data \mathbf{x} (Standard jackknife theory gives an approximate mean and variance in the case R(\mathbf{X}, F) = \theta(\hat{F}) - \theta(F), \thetasome parameter of interest.) A...