The jackknife

The jackknife is – like the bootstrap – a resampling method. The jackknife can be used to determine bias and standard error of estimators. It is simpler and faster than the bootstrap, since we do not draw new (bootstrap) samples, but we leave out one value from the original sample (for each jackknife sample). We just make estimations with one observation excluded.

The jackknife method was originally proposed by Quenouille (1949). Almost a century later, John Tukey (1958) extended the use of the method by showing how to use it for reducing the bias and estimating the variance. He invented the name "jackknife". Like a pocket knife, this technique can be used as an easy to use and fast to calculate "quick and dirty" tool that can solve a variety of problems. While the jackknife was very popular in the past because of its simplicity and fast computation, it generally has lower quality than the bootstrap, and it should be used only in rare, specific cases.

Let be an estimator for...