Designing Non-Parametric Estimates and Tests for Means

Karl Schlag

No ECO2006/26, Economics Working Papers from European University Institute

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.

Keywords: exact; distribution-free; nonparametric inference; binomial average; finite sample theory; Hannan consistency; universal consistent (search for similar items in EconPapers)
JEL-codes: C12 C14 C44 (search for similar items in EconPapers)
Date: 2006
New Economics Papers: this item is included in nep-ecm and nep-knm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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