High dimensional alpha test for linear factor pricing model with $L_q$-norm
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866911557970034688 |
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| author | Zhao, Ping Ma, Huifang Feng, Long |
| author_facet | Zhao, Ping Ma, Huifang Feng, Long |
| contents | We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is powerful under very sparse alternatives. To bridge these two regimes, we develop a class of $L_q$-based tests for finite $q$, including the practically useful $L_4$ and $L_6$ cases. We show that larger $q$ leads to greater sensitivity to sparse alternatives. We further establish the asymptotic independence between the $L_\infty$ statistic and the $L_q$ statistic for any finite $q$, which motivates a Cauchy combination test that adapts to a broad range of sparsity levels. Simulation studies and a real-data analysis show that the proposed methods are more robust to the unknown sparsity of the alternative and can outperform existing procedures in finite samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High dimensional alpha test for linear factor pricing model with $L_q$-norm Zhao, Ping Ma, Huifang Feng, Long Methodology We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is powerful under very sparse alternatives. To bridge these two regimes, we develop a class of $L_q$-based tests for finite $q$, including the practically useful $L_4$ and $L_6$ cases. We show that larger $q$ leads to greater sensitivity to sparse alternatives. We further establish the asymptotic independence between the $L_\infty$ statistic and the $L_q$ statistic for any finite $q$, which motivates a Cauchy combination test that adapts to a broad range of sparsity levels. Simulation studies and a real-data analysis show that the proposed methods are more robust to the unknown sparsity of the alternative and can outperform existing procedures in finite samples. |
| title | High dimensional alpha test for linear factor pricing model with $L_q$-norm |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.29764 |