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Designing Non-Parametric Estimates and Tests for Means

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  • Karl H. Schlag

Abstract

We show how to derive nonparametric estimates from results for Bernoulli distributions, provided the means are the only parameters of interest. The only information is that the support of each random variable is contained in a known bounded set. Examples include presenting minimax risk properties of the sample mean and a minimax regret estimate for costly treatment. With the same method we are able to design nonparametric exact statistical inference tests for means using existing uniformly most powerful (unbiased) tests for Bernoulli distributions. These tests are parameter most powerful in the sense that there is no alternative test with the same size that yields higher power over any set of alternatives that only depends on the means. As examples we present for the ?first time an exact unbiased nonparametric test for a single mean and for the equality of two means (both for independent samples and for paired experiments). We also show how to improve performance of Hannan consistent rules.

Suggested Citation

  • Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2006/26
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    References listed on IDEAS

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    1. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    2. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
    3. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    4. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
    5. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
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    Cited by:

    1. Karl H. Schlag, 2007. "How to Attain Minimax Risk with Applications to Distribution-Free Nonparametric Estimation and Testing," Economics Working Papers ECO2007/04, European University Institute.
    2. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
    3. Karl Schlag & Olivier Gossner, 2010. "Finite sample nonparametric tests for linear regressions," Economics Working Papers 1212, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Oliver Gossner & Karl Schlag, 2012. "Finite Sample Exact tests for Linear," Vienna Economics Papers 1201, University of Vienna, Department of Economics.

    More about this item

    Keywords

    exact; distribution-free; nonparametric inference; binomial average; finite sample theory; Hannan consistency; universal consistent;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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