Variable Selection Approaches in High-Dimensional Space

Abstract

Technological advancements in different fields such as molecular, imaging, and other laboratory tests have led to high-dimensional statistical problems. Variable selection in high-dimensional space is a critical step to identify a parsimonious model and improve the estimation accuracy of predictive models. The penalized likelihood approach has been extensively utilized to perform simultaneous variable selection and parameter estimation for the last decades. In this chapter, we present a brief review of the penalized likelihood approaches, with emphasis on the statistical properties and implementations for different outcomes with high-dimensional covariates. We also introduce independent screening procedures in ultra-high-dimensional variable selection. We then applied these selection methods to a high-dimensional setting in patients with a time-to-event outcome. We end the chapter with a brief review of high-dimensional inference.