The Annals of Statistics

A nonmanipulable test

Wojciech Olszewski and Alvaro Sandroni

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Abstract

A test is said to control for type I error if it is unlikely to reject the data-generating process. However, if it is possible to produce stochastic processes at random such that, for all possible future realizations of the data, the selected process is unlikely to be rejected, then the test is said to be manipulable. So, a manipulable test has essentially no capacity to reject a strategic expert.

Many tests proposed in the existing literature, including calibration tests, control for type I error but are manipulable. We construct a test that controls for type I error and is nonmanipulable.

Article information

Source
Ann. Statist., Volume 37, Number 2 (2009), 1013-1039.

Dates
First available in Project Euclid: 10 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1236693158

Digital Object Identifier
doi:10.1214/08-AOS597

Mathematical Reviews number (MathSciNet)
MR2502659

Zentralblatt MATH identifier
1162.62001

Subjects
Primary: 62A01: Foundations and philosophical topics
Secondary: 91A40: Game-theoretic models

Keywords
Test manipulation calibration model diagnostics

Citation

Olszewski, Wojciech; Sandroni, Alvaro. A nonmanipulable test. Ann. Statist. 37 (2009), no. 2, 1013--1039. doi:10.1214/08-AOS597. https://projecteuclid.org/euclid.aos/1236693158


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