Robust estimation of geomagnetic transfer functions

TLDR

The failure of statistical assumptions in estimating geomagnetic transfer functions is due to the finite spatial scale of many sources, and previous work has addressed this by hand‑selecting data segments believed to be free of source effects. The authors propose an automatic robust analysis scheme that accounts for the systematic increase of errors with increasing power and automatically downweights source‑contaminated outliers. The scheme achieves this by automatically downweighting outliers and adjusting for the power‑dependent error increase. Residual analysis shows that standard assumptions fail for periods from 5 min to several hours, yet the robust scheme consistently yields reliable transfer‑function estimates with realistic errors.

Abstract

We show, through an examination of residuals, that all of the statistical assumptions usually used in estimating transfer functions for geomagnetic induction data fail at periods from 5 min to several hours at geomagnetic mid-latitudes. This failure can be traced to the finite spatial scale of many sources. In the past, workers have tried to deal with this problem by hand selecting data segments thought to be free of source effects. We propose an automatic robust analysis scheme which accounts for the systematic increase of errors with increasing power and which automatically downweights source contaminated outliers. We demonstrate that, in contrast to ordinary least squares, this automatic procedure consistently yields reliable transfer function estimates with realistic errors.