Non-Gaussianity and direction dependent systematics in HST key project data

Abstract

Two new statistics, namely $\Delta_\chi^2$ and $\Delta_\chi$, based on extreme value theory, were derived in \cite{gupta08,gupta10}. We use these statistics to study direction dependence in the HST key project data which provides the most precise measurement of the Hubble constant. We also study the non-Gaussianity in this data set using these statistics. Our results for $\Delta_\chi^2$ show that the significance of direction dependent systematics is restricted to well below one $\sigma$ confidence limit, however, presence of non-Gaussian features is subtle. On the other hand $\Delta_\chi$ statistic, which is more sensitive to direction dependence, shows direction dependence systematics to be at slightly higher confidence level, and the presence of non-Gaussian features at a level similar to the $\Delta_\chi^2$ statistic.