The Crossing Statistic: Dealing with Unknown Errors in the Dispersion of
Type Ia Supernovae
ArXiv 1006.2141 (2010)
Authors:
Arman Shafieloo, Timothy Clifton, Pedro G Ferreira
Abstract:
We propose a new statistic that has been designed to be used in situations
where the intrinsic dispersion of a data set is not well known: The Crossing
Statistic. This statistic is in general less sensitive than `chi^2' to the
intrinsic dispersion of the data, and hence allows us to make progress in
distinguishing between different models using goodness of fit to the data even
when the errors involved are poorly understood. The proposed statistic makes
use of the shape and trends of a model's predictions in a quantifiable manner.
It is applicable to a variety of circumstances, although we consider it to be
especially well suited to the task of distinguishing between different
cosmological models using type Ia supernovae. We show that this statistic can
easily distinguish between different models in cases where the `chi^2'
statistic fails. We also show that the last mode of the Crossing Statistic is
identical to `chi^2', so that it can be considered as a generalization of
`chi^2'.
