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Jackknife Estimator: Simple Definition & Overview. Statistics Definitions >. The jackknife (“leave one out”) can be used to reduce bias and estimate standard errors. It is an alternative to the bootstrap method.
The jackknife technique can be used to estimate (and correct) the bias of an estimator calculated over the entire sample. Suppose θ {\displaystyle \theta } is the target parameter of interest, which is assumed to be some functional of the distribution of x {\displaystyle x} .
Here, we use the bootstrap function jackknife() to compute jackknife estimated standard errors for the plug-in estimates of the example functions - and we compare the jackknife standard errors with the delta method standard errors.
One of the earliest techniques to obtain reliable statistical estimators is the jackknife technique. It requires less computational power than more recent techniques. Suppose we have a sample x ( x , x ,..., 2. x ) and an estimator. ( x ) .
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we estimate the standard error of the estimator as • Unlike the bootstrap, the jackknife standard error estimate will not change for a given sample θ! (1),θ! (2),…,θ! (n) θ! se jack!=n−1 n (θ! (i)−θ! (.)) 2 i=1 n ∑
3.2.2 Jackknife Standard Error Estimation Consider what we usually do when estimating a mean of a distribution. We use the sample mean X= Xn i=1 X i as our estimator. To see the relationship with jackknife estimation, we can write the mean with the ith observation removed as X (i) as: X (i) = P n j=1 X j X i n 1 Therefore an individual X i can ...
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Enter the jackknife. It provides an alternative and reasonably robust method for determining the propagation of error from the data to the parameters. Starting from a sample of measurements, the jackknife begins by throwing out the first measurement, leaving a jackknife data set of ``resampled'' values.
