Which variables are more important for high-dimensional regression?

What is it about?

In high-dimensional regression, a critical component of modeling is the choice of the right variables into statistical models. Also, for decision-making, it is very helpful to know which variables are most important for predicting or explaining the response variable. This paper proposes a variable importance measure that is shown to work well reliably.

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Why is it important?

Variable importance is of interest on its own for decision-making. For instance, if two variables are similarly important but one is much cheaper to obtain/operate on, when parsimony is desired due to various reasons, we may use the variable importance information to drop one properly. Also, knowing variable importance information can help improve reliability of modeling. Currently, there is too much variable/model selection uncertainty in statistical applications, especially in high-dimensional sparse estimation, variable importance measures are valuable to enhance quality of data analysis and improve reproducibility of statistical results.