  We analyze bias correction methods using jackknife, bootstrap, and Taylor
series. We focus on the binomial model, and consider the problem of bias
correction for estimating $f(p)$, where $f \in C[0,1]$ is arbitrary. We
characterize the supremum norm of the bias of general jackknife and bootstrap
estimators for any continuous functions, and demonstrate the in delete-$d$
jackknife, different values of $d$ may lead to drastically different behaviors
in jackknife. We show that in the binomial model, iterating the bootstrap bias
correction infinitely many times may lead to divergence of bias and variance,
and demonstrate that the bias properties of the bootstrap bias corrected
estimator after $r-1$ rounds are of the same order as that of the $r$-jackknife
estimator if a bounded coefficients condition is satisfied.
