High-dimensional tests for elliptical models are created by testing radial-directional independence after standardization, with adaptive sum/max/Cauchy statistics and proven asymptotic properties.
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Parameter-free first-order methods attain optimal oracle complexity O(ε^{-2/(1+3ρ)}) for convex function-constrained optimization under Hölder smoothness by combining modified Polyak steps, Nesterov momentum, and APL level-set methods.
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High-Dimensional Tests for Elliptical Models via Radial--Directional Dependence
High-dimensional tests for elliptical models are created by testing radial-directional independence after standardization, with adaptive sum/max/Cauchy statistics and proven asymptotic properties.
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Uniformly Optimal and Parameter-free First-order Methods for Convex and Function-constrained Optimization
Parameter-free first-order methods attain optimal oracle complexity O(ε^{-2/(1+3ρ)}) for convex function-constrained optimization under Hölder smoothness by combining modified Polyak steps, Nesterov momentum, and APL level-set methods.