Sure independence screening for covariate-dependent extreme value index estimation

Abstract

One of the main topics in extreme value analysis is the estimation of the extreme value index, which characterizes the tail behavior of a distribution. Although covariate dependent extreme value index estimation has been widely studied, covariate screening for high-dimensional covariates has not been fully investigated. This paper proposes a sure independence screening method for covariate-dependent extreme value index estimation. The proposed method ranks covariates by marginal utilities constructed from a kernel-based conditional Pickands estimator. Unlike ordinary local smoothing, the proposed screening procedure uses a large-bandwidth kernel regime to obtain stable marginal contrasts. We establish the sure screening property under this regime, showing that all truly active covariates are retained with probability tending to one. Simulation studies and a real-data application demonstrate the effectiveness of the proposed method.