Jackknife (statistics)

Jack Knife is in the statistics a method of resampling. Jackknife is used to estimate the random error of an estimation method, and possible distortion (English bias). Jackknife is a special case of bootstrapping. The method was first published in 1956 and 1958 by MH Quenouille and John W. Tukey. The name should emphasize the general applicability of the method for statistical purposes.

Method

Frequently Jackknife is equated with delete- 1 jackknife. In each case, a value is omitted from the original sample and calculates the estimate of this reduced sample. If from the original sample not only a value is omitted, but a lot of d, then one speaks of delete- d jackknife. By eliminating d from a total of N values ​​, different reduced samples may be generated which have many values ​​.

In the following, the delete- 1 jackknife method is described. The mean of the reduced jackknife sample i, which is produced by sweeping the value is:

And the mean of the original sample would. Then the average of all jackknife sample is given by:

The variance of the sample can now be estimated by:

The jackknife method provides for the bias the value: