Jackknife method
The jackknife method ( English 'pocket knife') is a method of resampling in statistics . Jackknife is used to the random error of an estimation method and a possible distortion (engl. Bias ) to estimate. The jackknife method is a special case of the bootstrapping process . The method was first published in 1956 and 1958 by MH Quenouille and John W. Tukey . The name is intended to emphasize the general applicability of the method for statistical purposes.
method
Jackknife is often equated with delete-1 Jackknife . In this case, from the original sample in each case a value is calculated is omitted and the estimator for this reduced sample. If not just one value is omitted from the original sample, but d many, then one speaks of delete-d jackknife . By omitting total values, different reduced samples can be generated that have many values.
The following describes the delete-1 jackknife method. The mean value of the reduced jackknife sample i, which results from deleting the value , is:
and be the mean of the original sample . Then the mean value over all Jackknife samples is given by:
- .
The variance of the estimator can now be estimated by:
- .
The Jackknife method returns the value for the bias of the estimator :
literature
Joseph Lee Rodgers: The Bootstrap, the Jackknife, and the Randomization Test: A Sampling Taxonomy . Multivariate Behavioral Research, 34, No. 4 pp. 441ff (1999)