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Bringing Game Theory to Hypothesis Testing: Establishing Finite Sample Bounds on Inference

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Author Info
Karl Schlag ()

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Abstract

Small sample properties are of fundamental interest when only limited data is avail- able. Exact inference is limited by constraints imposed by speci.c nonrandomized tests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature. We use this method to investigate sequential tests for the di¤erence between two means when outcomes are constrained to belong to a given bounded set. Tests of inequality and of noninferiority are included. We .nd that inference in terms of type II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

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Publisher Info
Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1099.

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Date of creation: Jun 2008
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Handle: RePEc:upf:upfgen:1099

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Web page: http://www.econ.upf.edu/

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Related research
Keywords: Exact; distribution-free; nonparametric; independent samples; matched pairs; Z test; unavoidable type II error; noninferiority; LeeX;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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  1. Karl Schlag, 2008. "A New Method for Constructing Exact Tests without Making any Assumptions," Economics Working Papers 1109, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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