High-Dimensional Tests for Elliptical Models via Radial--Directional Dependence

Abstract

We develop high-dimensional goodness-of-fit tests for elliptical models by testing radial--directional independence after affine standardization. The method forms coordinatewise correlations between the log-radius and directional components, using a sum statistic for dense departures, a max statistic for sparse departures, and a Cauchy combination for adaptation. We derive oracle null limits, prove asymptotic independence of the sum and max components under both the null and a balanced local alternative, and establish validity of high-dimensional Hettmansperger--Randles plug-in standardization under explicit perturbation rates. Simulations and data analyses show stable size control, dense--sparse power complementarity, and interpretable coordinate-level diagnostics.