Nabil Bouamara, Sébastien Laurent, Shuping Shi
arXiv 23 Mar 2023 · Econometrics
arXiv:2303.13406 · PDF · DOI · OpenAlex · Extracted main text
We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test recursively on a sequence of expanding subsets of $p$-values and is referred to as the sequential Cauchy combination test. While the original Cauchy combination test aims to make a global statement about a set of null hypotheses by summing transformed $p$-values, our sequential version determines which $p$-values trigger the rejection of the global null. The sequential test achieves strong familywise error rate control, exhibits less conservatism compared to existing controlling procedures when dealing with dependent test statistics, and provides a power boost. As illustrations, we revisit two well-known large-scale multiple testing problems in finance for which the test statistics have either serial dependence or cross-sectional dependence, namely monitoring drift bursts in asset prices and searching for assets with a nonzero alpha. In both applications, the sequential Cauchy combination test proves to be a preferable alternative. It overcomes many of the drawbacks inherent to inequality-based controlling procedures, extreme value approaches, resampling and screening methods, and it improves the power in simulations, leading to distinct empirical outcomes.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Christensen, K., R. C. Oomen, and R. Renò (2022) The drift burst hypothesis | 1.000 | 12 | 4 | 100% |
| 2 | Fan, J., Y. Liao, and J. Yao (2015) Power enhancement in high-dimensional cross-sectional tests | 1.000 | 7 | 3 | 100% |
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| 4 | Fama, E. F. and K. R. French (2015) A five-factor asset pricing model | 1.000 | 5 | 3 | 100% |
| 5 | Liu, Y. and J. Xie (2020) Cauchy combination test: A powerful test with analytic $p$-value calculation under arbitrary dependency structures | 0.977 | 15 | 6 | 93% |
| 6 | Hochberg, Y (1988) A sharper Bonferroni procedure for multiple tests of significance | 0.928 | 4 | 3 | 100% |
| 7 | Holm, S (1979) A simple sequentially rejective multiple test procedure | 0.928 | 4 | 3 | 100% |
| 8 | Giglio, S., Y. Liao, and D. Xiu (2021) Thousands of alpha tests | 0.874 | 10 | 2 | 100% |
| 9 | Barras, L., O. Scaillet, and R. Wermers (2010) False discoveries in mutual fund performance: Measuring luck in estimated alphas | 0.811 | 4 | 2 | 100% |
| 10 | Lee, S. S. and P. A. Mykland (2008) Jumps in financial markets: A new nonparametric test and jump dynamics | 0.585 | 3 | 1 | 100% |
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