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

Two new statistics, namely $Δ_χ^2$ and $Δ_χ$, 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 $Δ_χ^2$ show that the significance of direction dependent systematics is restricted to well below one $σ$ confidence limit, however, presence of non-Gaussian features is subtle. On the other hand $Δ_χ$ 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 $Δ_χ^2$ statistic.

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