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.

翻译：本文研究高维线性因子定价模型的alpha检验问题。我们提出了一种基于空间符号的极大值型检验方法以处理稀疏备择假设情形。此外，我们证明了该检验与Liu等人（2023）提出的基于空间符号的求和型检验具有渐近独立性。基于这一结果，我们引入了一种结合极大值型与求和型检验的柯西组合检验程序。模拟研究与实际数据应用表明，新提出的检验程序不仅对重尾分布具有稳健性，同时对备择假设的稀疏性也具有稳健性。