Cramér-Rao bound and Rao-Blackwell theorem
Cota de Cramér-Rao y teorema de Rao-Blackwell
- Date
- 1945 · confidence high
- Place
- Indian Statistical Institute, Calcutta (Kolkata), West Bengal, India
- Credited to
- Calyampudi Radhakrishna Rao
- People
- 👤 Calyampudi Radhakrishna Rao1920–2023
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
In a single 1945 paper, Rao showed that no unbiased estimator can have a variance smaller than the inverse of the Fisher information, and how to improve any estimator by conditioning it on a sufficient statistic. He also introduced information geometry.
The bound was obtained independently by Cramér (1946), Fréchet (1943) and Darmois (1945); Blackwell published his theorem in 1947.
What it led to
- modern estimation theory
- information geometry
- limits of precision in physics, engineering and signal processing