# Jackknife¶

The jaccknife method aims at computing an unbiased estimate of the error bar on an observable $$f(\langle X \rangle, \langle Y \rangle)$$ when $$f$$ is nonlinear in its variables.

The jackknifed series is defined from the original series $$\lbrace x_i \rbrace _{i=1\dots N}$$ as:

$x_i^J = \frac{1}{N} \sum_{j=1,j\neq i}^{N} x_j$

The error estimate is then:

$\Delta f(\langle X\rangle) = \sqrt{(N-1) \sigma_{f^J}^2}$

where $$f^J_i = f(x_i^J)$$ and $$\sigma_{f^J}^2$$ is the variance of this series.

## Synopsis¶

make_jackknife(T series)
• series: object with TimeSeries concept

returns the jackknifed time series.

## Example¶

#include <triqs/statistics.hpp>
using namespace triqs::statistics;
int main() {
observable<double> A;
A << 1.;
A << 1.5;
A << .2;
A << 1.1;
auto A_j = make_jackknife(A);
std::cout << A_j << std::endl;
return 0;
}