Designing Non-Parametric Estimates and Tests for Means

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Designing Non-Parametric Estimates and Tests for Means

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Karl H. Schlag

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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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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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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

This paper has been announced in the following NEP Reports:

NEP-ALL-2006-09-16 (All new papers)
NEP-ECM-2006-09-16 (Econometrics)
NEP-KNM-2006-09-16 (Knowledge Management & Knowledge Economy)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May. [Downloadable!] (restricted)
Other versions:
- Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000. [Downloadable!]
- Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptative Strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute. [Downloadable!]
Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, 07. [Downloadable!] (restricted)
Other versions:
- Charles Manski, 2003. "Statistical treatment rules for heterogeneous populations," CeMMAP working papers CWP03/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
Other versions:
- Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997. [Downloadable!]
- 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. [Downloadable!]

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

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. [Downloadable!]

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