The jackknife is a resampling statistics method that repeatedly recomputes an estimator after
deleting one observation. Let 
be an estimator based on a sample
of size 
,
let 
denote the same estimator
computed after omitting observation 
, and define
 |
(1)
|
The jackknife estimate of bias is
 |
(2)
|
giving the bias-corrected estimate
 |
(3)
|
The corresponding jackknife estimate of variance is
 |
(4)
|
The delete-one jackknife is most effective for estimators that change smoothly with the empirical distribution function. It can perform poorly for nonsmooth statistics, statistics determined by extreme observations, or dependent data. Block and delete-more-than-one variants are used in some such settings.
