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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.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/26.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/26

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Related research

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

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References

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  1. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  2. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
  3. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
  4. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  5. Charles Manski, 2003. "Statistical treatment rules for heterogeneous populations," CeMMAP working papers CWP03/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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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. Oliver Gossner & Karl Schlag, 2012. "Finite Sample Exact tests for Linear," Vienna Economics Papers 1201, University of Vienna, Department of Economics.
  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. 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.

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