Double Robust high dimensional alpha test for linear factor pricing model

TL;DR

This paper introduces a robust high-dimensional alpha testing method for linear factor pricing models, combining max-type and sum-type tests to effectively handle sparsity and heavy-tailed distributions.

Contribution

It proposes a novel Cauchy Combination test that merges spatial sign-based max and sum tests, improving robustness in high-dimensional settings.

Findings

The combined test is asymptotically independent of existing tests.

Simulation studies show robustness against heavy-tailed distributions.

Real data applications confirm improved performance in sparse scenarios.

Abstract

In this paper, we investigate alpha testing for high-dimensional linear factor pricing models. We propose a spatial sign-based max-type test to handle sparse alternative cases. Additionally, we prove that this test is asymptotically independent of the spatial-sign-based sum-type test proposed by Liu et al. (2023). Based on this result, we introduce a Cauchy Combination test procedure that combines both the max-type and sum-type tests. Simulation studies and real data applications demonstrate that the new proposed test procedure is robust not only for heavy-tailed distributions but also for the sparsity of the alternative hypothesis.