Statistical Revision of the Moment Method

Abstract

The moment method is a well known technique, which uses a time series ofthe first 3 moments of a spectral line, to estimate the (discrete) modeparameters ℓ and m. The method, contrary to Doppler imaging,also yields other interesting(real-valued) parameters such as the inclination angle i, or v sin i,during its identification procedure.In this paper, we are not only interested in the estimation of thesereal-valued parameters themselves but also inreliable estimates for their uncertainty.We designed a statistical formalism for the moment method based on theso-called generalized estimating equations (GEE). This formalismaims to estimate the uncertainty of the real-valued parameters taking intoaccount that the different moments of a line profile are correlated and –more importantly – that the uncertainty of the observed moments depends onthe pulsation parameters. The latter property of the moment method makesthe least-squares technique a poor choice to estimate the uncertainty ofthe real-valued parameters. We implemented the GEE method and presentan application to a high-resolution spectroscopic dataset of the slowly pulsating B star HD181558.