Jack-knife resampling

Jackknife resampling is a statistical technique whereby you calculate an estimate of a statistic from a sample leaving out one data point from your sample. You then do that for all values within your sample and calculate the average of all your calculated statistics.

The best way to describe what is jackknife resampling is with an example. Suppose we have the following sample of data

[10,20,30]

and we want to calculate the "jackknifed" mean.

What we would do is calculate the mean from this dataset with one of the values missing. For example,

X1 = (20 + 30) / 2 = 25

where :

X1 - sample mean with one value removed and the observation value '10' has been removed.

We do this for all of our values within the sample so that we have:

X1 = (20 + 30) / 2 = 25

X2 = (10 + 30) / 2 = 20

X3 = 10 + 20 / 2 = 15

The final step is to calculate the mean of all our resamples (e.g find the mean of X1, X2, X3) s.t

Mean = (X1 + X2 + X3)/3

Mean = (25 + 20 + 15)/3

Mean = 20

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