Efficient Federated Estimation and Inference for High-Dimensional Tail Index Regression

2026-06-02

AI Summary

This study addresses the challenge of tail index regression for high-dimensional heavy-tailed data in heterogeneous federated settings under privacy or regulatory constraints, where existing methods struggle to simultaneously handle data heterogeneity and variable selection. The authors propose a personalized federated framework that integrates sparse regularization with non-convex fusion penalties to jointly perform coefficient estimation, variable selection, and recovery of latent client groups. They innovatively design an ADMM-based federated optimization algorithm coupled with an adaptive weighted debiased inference procedure, enabling, for the first time in federated learning, simultaneous estimation and statistical inference for high-dimensional tail index regression. Theoretical analysis establishes non-asymptotic convergence rates and oracle properties for the proposed estimator, while experiments demonstrate its superior performance in estimation accuracy, group recovery, and inference efficiency.

Abstract

Tail index regression studies how covariates affect tail heaviness in heavy-tailed data. In many applications, data are distributed across heterogeneous sources, where direct pooling is infeasible due to privacy or regulatory constraints. Existing methods mainly focus on single-dataset analysis and do not address heterogeneous federated settings. We develop a personalized federated framework for high-dimensional tail index regression that accommodates client heterogeneity while exploiting latent similarities across clients. The proposed estimator combines sparsity regularization with nonconcave fusion penalties to perform coefficient estimation, variable selection, and group recovery. We establish non-asymptotic convergence rates and show that the estimator enjoys an oracle property by consistently recovering the underlying grouping structure. For computation, we develop an ADMM-based federated algorithm with adaptive gradient updates and establish its convergence guarantees. We further propose a debiased federated inference procedure based on adaptive weighted aggregation across related clients, yielding valid confidence intervals and hypothesis tests with improved efficiency over target-only inference. Simulation studies and real-data analysis demonstrate the effectiveness of the proposed methods.

Problem

• federated learning
• tail index regression
• high-dimensional statistics
• data heterogeneity
• privacy constraints

Innovation

• federated learning
• tail index regression
• nonconcave fusion penalty
• high-dimensional inference
• ADMM algorithm