## The Annals of Statistics

### Minimax Tests and the Neyman-Pearson Lemma for Capacities

#### Abstract

Robust test problems between two approximately known simple hypotheses can be formalized as minimax test problems between two composite hypotheses. We show that if the composite hypotheses can be described in terms of alternating capacities of order 2 (in the sense of Choquet), then the minimax tests are ordinary Neyman-Pearson tests between a fixed representative pair of simple hypotheses; moreover, the condition is in a certain sense also necessary. All the neighborhoods customarily used to formalized approximate knowledge happen to have this particular structure.

#### Article information

Source
Ann. Statist. Volume 1, Number 2 (1973), 251-263.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176342363

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176342363

Mathematical Reviews number (MathSciNet)
MR356306

Zentralblatt MATH identifier
0259.62008

#### Citation

Huber, Peter J.; Strassen, Volker. Minimax Tests and the Neyman-Pearson Lemma for Capacities. Ann. Statist. 1 (1973), no. 2, 251--263. doi:10.1214/aos/1176342363. http://projecteuclid.org/euclid.aos/1176342363.

#### Corrections

• See Correction: Peter J. Huber, Volker Strassen. Note: Correction to Minimax Tests and the Neyman-Pearson Lemma for Capacities. Ann. Statist., Volume 2, Number 1 (1974), 223--224.