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Implement Jackknife Using Parallel Computing

This example is from the jackknife function reference page, but runs in parallel.

Generate a sample data of size 10000 from a normal distribution with mean 0 and standard deviation 5.

sigma = 5;
rng('default')
y = normrnd(0,sigma,10000,1);

Run jackknife in parallel to estimate the variance. To do this, use statset to create the options structure and set the UseParallel field to true.

opts = statset('UseParallel',true);
m = jackknife(@var,y,1,'Options',opts);

Compare the known bias formula with the jackknife bias estimate.

n = length(y);
bias = -sigma^2/n % Known bias formula
jbias = (n-1)*(mean(m)-var(y,1)) % jackknife bias estimate
Starting parallel pool (parpool) using the 'local' profile ...

Connected to the parallel pool (number of workers: 6).

bias =

   -0.0025


jbias =

   -0.0025

Compare how long it takes to compute in serial and in parallel.

tic;m = jackknife(@var,y,1);toc  % Serial computation
Elapsed time is 1.638026 seconds.
tic;m = jackknife(@var,y,1,'Options',opts);toc % Parallel computation
Elapsed time is 0.507961 seconds.

jackknife does not use random numbers, so gives the same results every time, whether run in parallel or serial.