Robust High Dimensional Alpha Test for Linear Factor Pricing Model

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 detect sparse alternatives. Additionally, the asymptotic independence between this test and the existing spatial‐sign‐based sum‐type test is established. 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 proposed test procedure is robust to heavy‐tailed distributions and powerful against alternatives with different sparsity levels.