A Nonmanipulable Test

Wojciech Olszewski · Alvaro Sandroni

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Game Theory and Applications Forecasting Techniques and Applications Sports Analytics and Performance

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.

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References

1989Maxmin expected utility with non-unique prior 2006Prediction, Learning, and Games 2007Probabilistic Forecasts, Calibration and Sharpness 1953Minimax Theorems 2003Calibration with Many Checking Rules 2003The reproducible properties of correct forecasts 2001Any Inspection is Manipulable 1999An Easier Way to Calibrate

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2010Testing theories with learnable and predictive representations

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