Benjamini–Hochberg controls the false discovery rate
Theorem taught in High-dimensional analysis, part of Statistical learning
Benjamini–Hochberg controls the false discovery rate
| Type | Theorem |
| Taught in | High-dimensional analysis |
| Part | Statistical learning |
Suppose the p-values are mutually independent and each true-null p-value is valid: \mathbb{P}(P_i\le t)\le t for 0\le t\le 1. The procedure at q^*\in(0,1) satisfies
\mathrm{FDR}\le\frac{m_0}{m}q^*\le q^*.
Equality holds in the first inequality for exactly uniform null p-values (Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001).
Used in
- Taught in High-dimensional analysis, where the derivation and examples are.
- All 9 questions on High-dimensional analysis
See also
Rank bound · Family-wise control implies false-discovery control · Benjamini–Hochberg · Why classical methods fail when p > n · Rank of the sample covariance · Regression when p > n · Where high-dimensional columns come from · Questions to ask of high-dimensional data