Designing Non-Parametric Estimates and Tests for Means
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.
|Date of creation:||2006|
|Date of revision:|
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- Sergiu Hart & Andreu Mas-Colell, 1997.
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Game Theory and Information
9703006, EconWPA, revised 24 Mar 1997.
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- 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.
- S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
- Charles F. Manski, 2003.
"Statistical treatment rules for heterogeneous populations,"
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- Sergiu Hart & Andreu Mas-Colell, 1999.
"A General Class of Adaptive Strategies,"
Game Theory and Information
9904001, EconWPA, revised 23 Mar 2000.
- Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
- Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
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