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April 2009 A nonmanipulable test
Wojciech Olszewski, Alvaro Sandroni
Ann. Statist. 37(2): 1013-1039 (April 2009). DOI: 10.1214/08-AOS597


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.


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Wojciech Olszewski. Alvaro Sandroni. "A nonmanipulable test." Ann. Statist. 37 (2) 1013 - 1039, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62001
MathSciNet: MR2502659
Digital Object Identifier: 10.1214/08-AOS597

Primary: 62A01
Secondary: 91A40

Keywords: Calibration , model diagnostics , Test manipulation

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 2 • April 2009
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