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Designing Non-Parametric Estimates and Tests for Means
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1725-6704
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EUI ECO; 2006/26
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SCHLAG, Karl H., Designing Non-Parametric Estimates and Tests for Means, EUI ECO, 2006/26 - https://hdl.handle.net/1814/6090
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.