## The Annals of Statistics

- Ann. Statist.
- Volume 10, Number 1 (1982), 226-232.

### Binary Experiments, Minimax Tests and 2-Alternating Capacities

#### Abstract

The concept of Choquet's 2-alternating capacity is explored from the viewpoint of Le Cam's experiment theory. It is shown that there always exists a least informative binary experiment for two sets of probability measures generated by 2-alternating capacities. This result easily implies the Neyman-Pearson lemma for capacities. Moreover, its proof gives a new method of construction of minimax tests for problems in which hypotheses are generated by 2-alternating capacities. It is also proved that the existence of least informative binary experiments is sufficient for a set of probability measures to be generated by a 2-alternating capacity. This gives a new characterization of 2-alternating capacities, closely related to that of Huber and Strassen.

#### Article information

**Source**

Ann. Statist., Volume 10, Number 1 (1982), 226-232.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345705

**Digital Object Identifier**

doi:10.1214/aos/1176345705

**Mathematical Reviews number (MathSciNet)**

MR642734

**Zentralblatt MATH identifier**

0496.62004

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G35: Robustness

Secondary: 62B15: Theory of statistical experiments

**Keywords**

Robust testing minimax testing capacities binary experiments

#### Citation

Bednarski, Tadeusz. Binary Experiments, Minimax Tests and 2-Alternating Capacities. Ann. Statist. 10 (1982), no. 1, 226--232. doi:10.1214/aos/1176345705. https://projecteuclid.org/euclid.aos/1176345705