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;
}