Robust Spatial-Sign-Based Testing of High-Dimensional Alpha in Conditional Factor Models

2026-04-13

AI Summary

This study addresses the hypothesis testing problem for alpha in high-dimensional factor pricing models with time-varying coefficients, proposing an adaptive testing procedure that simultaneously accommodates sparsity and robustness to heavy-tailed errors. The method integrates max- and sum-type statistics based on spatial signs and employs a Cauchy combination framework to construct the test. Its key theoretical contribution lies in establishing, for the first time, the asymptotic independence of these two types of statistics in high dimensions, which ensures optimal power across diverse sparsity patterns. Extensive simulations and empirical analyses demonstrate that the proposed approach consistently outperforms competing methods under various alternative hypotheses and exhibits strong robustness against heavy-tailed disturbances.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper develops a new framework for alpha testing in high-dimensional factor pricing models with time-varying coefficients. To detect sparse alternatives, we propose a spatial-sign-based max-type test and derive its limiting null distribution. A key theoretical result is that our statistic is asymptotically independent of the spatial-sign-based sum-type test proposed by Zhao (2023). Exploiting this independence, we construct an adaptive testing procedure via the Cauchy combination method. This approach integrates the complementary strengths of both max-type and sum-type statistics, ensuring robust power across diverse sparsity levels. Extensive simulations and an empirical application demonstrate that the proposed test is resilient to heavy-tailed distributions and maintains superior performance under various alternative specifications.

Problem

• alpha testing
• high-dimensional factor models
• spatial-sign
• sparse alternatives
• heavy-tailed distributions

Innovation

• spatial-sign
• max-type test
• adaptive testing
• Cauchy combination
• high-dimensional alpha testing