Variable screening based on Gaussian Centered L-moments

TL;DR

This paper introduces Gaussian Centered L-moments, a robust statistical measure for variable screening in big data, especially effective in identifying non-standard distributions while addressing outlier sensitivity.

Contribution

The paper proposes Gaussian Centered L-moments, a novel modification of L-moments that are zero at Gaussian distributions, improving variable screening accuracy.

Findings

Effective in screening important genes in cancer genetics data.

Outperforms conventional moments in robustness and distributional shape detection.

Theoretically justified and practically validated.

Abstract

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.