  An important challenge in big data is identification of important variables.
In this paper, we propose methods of discovering variables with non-standard
univariate marginal distributions. The conventional moments-based summary
statistics can be well-adopted for that purpose, but their sensitivity to
outliers can lead to selection based on a few outliers rather than
distributional shape such as bimodality. To address this type of
non-robustness, we consider the L-moments. Using these in practice, however,
has a limitation because they do not take zero values at the Gaussian
distributions to which the shape of a marginal distribution is most naturally
compared. As a remedy, we propose Gaussian Centered L-moments which share
advantages of the L-moments but have zeros at the Gaussian distributions. The
strength of Gaussian Centered L-moments over other conventional moments is
shown in theoretical and practical aspects such as their performances in
screening important genes in cancer genetics data.
