The bootstrap method in space physics: Error estimation for the minimum variance analysis

The minimum variance analysis technique introduced by Sonnerup and Cahill (1967) is a useful tool in space physics. However the statistical errors appearing in this method are difficult to estimate accurately because of the complicated form of the eigenvalue decomposition. To deal with this problem, this paper introduces the bootstrap method (Efron, 1979) which replaces analytical solutions with repeated simple calculations. We apply this method to the estimation of the statistical errors in the minimum variance direction and the average component in the minimum variance direction, and show that this method accurately estimates the errors.