perform jackknife on array in matlab

Jackknife is a resampling technique that is used to estimate the bias and other statistical properties of an estimator. Here is how you can perform Jackknife on an array in matlab:

main.m
% Create an example array
arr = [1, 2, 3, 4, 5];

% Perform Jackknife
n = length(arr);
jstat = zeros(n, 1);
for i = 1:n
    idx = (1:n) ~= i;
    jackknife_data = arr(idx);
    jstat(i) = mean(jackknife_data); % calculate the statistic of interest
end

% Calculate the Jackknife Bias
bias = (n - 1) * (mean(jstat) - mean(arr));
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In the above code, we first create an example array arr. Then we perform jackknife by looping over each element of the array and leaving it out of the analysis. For each iteration, we calculate the statistic of interest, in this case, the mean of the remaining elements in the array. We save these statistics in the jstat vector. Finally, we calculate the Jackknife bias by averaging the statistic estimates and subtracting the overall mean from this average.

Note that this example code is assuming that the estimator of interest is the mean. In practice, this estimator could be any function of the data.

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