A computer-intensive resampling method for the estimation of an unknown parameter of a distribution while making minimal assumptions. In this respect it resembles the bootstrap. Denote the parameter by θ and its usual estimate, based on a sample of n observations, by θ̂. For example, if the parameter were the mean of a distribution then the usual estimate would be the sample mean.
The jackknife procedure produces an alternative estimate θ~, together with an estimate of the bias (see estimator) of the usual estimate. Let θ̂−j be the usual estimate of θ calculated from the same sample but with the jth observation omitted. Now define the pseudovalue θ~j by
The jackknife mean θ~ and variance s2 are given by
The estimated bias is θ̂−θ~. The ratio
has an approximate standard normal distribution. The method also applies to the estimation of more complex characteristics, such as the correlation in a set of bivariate observations. The term jackknife was coined by Tukey in the early 1960s.
A statistical technique in which, given a data set with n observations, the analysis is recalculated n times omitting each observation in turn (removed with a ‘jackknife’). The mean and variance of the estimated parameters in the model may be compared with those obtained from the full set. The method is related to statistical bootstrap estimation.
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- Micronesia, Federated States of
- micron(symbol: μ)
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