Jackknife-After-Bootstrap

We are familiar with a bootstrap estimate of a statistical parameter, such as standard error. Since bootstrap is the estimate, it also has its own error. How can we calculate the bootstrap error? The answer is, ..using jackknife.

load law
lsat=law(:,1);
gpa=law(:,2);
B=1000;

%bootstrap
[bootstat,bootsam]=bootstrp(B,'corrcoef',lsat,gpa);
n=length(gpa);
jreps=zeros(1,n);

%jackknife
for i=1:n
    [I,J]=find(bootsam==i);
    %remove column containing i-th sample,
    jacksam=setxor(J,1:B);
    bootrep=bootstat(jacksam,2);
    jreps(i)=std(bootrep);
end
varjack = (n-1)/n * sum((jreps-mean(jreps)).^2);
sejack = sqrt(varjack)
gamma=std(bootstat(:,2))

gamma =
    0.1332

sejack =
    0.0839

The result can be interpreted as follows. The standard error of the correlation coefficient for this simulation is $\hat\gamma_B=\hat{SE}_{Boot}(\hat\rho)=0.133$ and the estimated error of this value is $\hat{SE}_{Jack}(\hat\gamma_B)=0.084$.