Chernoff-consistent

by W. B. Meitei, PhD

A statistical procedure is called Chernoff-consistent if, as the sample size grows, the probabilities of both Type I error (false positive) and Type II error (false negative) approach zero, meaning the test almost surely makes the correct decision for large sample sizes. In other words, the test's power (probability of correctly rejecting a false null) and its specificity (probability of correctly not rejecting a true null) both converge to one as data accrues.

"Chernoff-consistency" is stronger than just requiring that one type of error vanish; it requires both errors to vanish asymptotically. The concept comes from Herman Chernoff's work in statistical hypothesis testing, which established the optimal rates at which errors can decrease with increasing sample size.

In the context of recent statistical methodology, such as "cake priors," tests are described as Chernoff-consistent if they guarantee, with sufficient data, that incorrect decisions become exceedingly rare, addressing issues like the Bartlett-Lindley-Jeffreys paradox by ensuring both types of inference errors disappear in the limit.

Suggested Readings:

1. Li, W., & Xie, W. (2024). Efficient estimation of the quantum Chernoff bound. Physical Review A, 110(2), 022415.
2. Tslil, O., Lehrer, N., & Carmi, A. (2020). Approaches to Chernoff fusion with applications to distributed estimation. Digital Signal Processing, 107, 102877.
3. Kuszmaul, W. (2025). A Simple and Combinatorial Approach to Proving Chernoff Bounds and Their Generalizations. Symposium on Simplicity in Algorithms (SOSA) (pp. 77-93). Society for Industrial and Applied Mathematics.
4. Rao, A. (2018). Lecture 21: The Chernoff Bound.
5. Williamson, D. P. (2016). Cherno bounds. ORIE 6334 Spectral Graph Theory.

Suggested Citation: Meitei, W. B. (2025). Chernoff-consistent. WBM STATS.