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A New Method for Constructing Exact Tests without Making any Assumptions

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Author Info
Karl Schlag ()

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Abstract

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with finitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create confidence intervals for the difference between two means (or variances) and tests of stochastic inequality and correlation.

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File URL: http://www.econ.upf.edu/docs/papers/downloads/1109.pdf
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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 1109.

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Date of creation: Aug 2008
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Handle: RePEc:upf:upfgen:1109

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

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Related research
Keywords: Distribution-free; nonparametric; exact hypothesis testing; unavoidable inaccuracy; nonparametric Behrens-Fisher problem; UMPU test; Kendall's tau; Qn;

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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. Djankov, Simeon & La Porta, Rafael & Lopez-de-Silanes, Florencio & Shleifer, Andrei, 2008. "The law and economics of self-dealing," Journal of Financial Economics, Elsevier, vol. 88(3), pages 430-465, June. [Downloadable!] (restricted)
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  2. Karl Schlag, 2008. "Bringing Game Theory to Hypothesis Testing: Establishing Finite Sample Bounds on Inference," Economics Working Papers 1099, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  3. Rachel Croson & Nancy Buchan, 1999. "Gender and Culture: International Experimental Evidence from Trust Games," American Economic Review, American Economic Association, vol. 89(2), pages 386-391, May. [Downloadable!] (restricted)
  4. Fishman, George S., 1991. "Confidence intervals for the mean in the bounded case," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 223-227, September. [Downloadable!] (restricted)
  5. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer, vol. 12(2), pages 153-157, June. [Downloadable!] (restricted)
  6. Reiczigel, Jeno & Zakarias, Ildiko & Rozsa, Lajos, 2005. "A Bootstrap Test of Stochastic Equality of Two Populations," The American Statistician, American Statistical Association, vol. 59, pages 156-161, May. [Downloadable!] (restricted)
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