How to Attain Minimax Risk with Applications to Distribution-Free Nonparametric Estimation and Testing

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dc.contributor.author SCHLAG, Karl H.
dc.date.accessioned 2007-03-26T10:46:30Z
dc.date.available 2007-03-26T10:46:30Z
dc.date.issued 2007
dc.identifier.issn 1725-6704
dc.identifier.uri http://hdl.handle.net/1814/6757
dc.description.abstract We show how to a derive exact distribution-free nonparametric results for minimax risk when underlying random variables have known finite bounds and means are the only parameters of interest. Transform the data with a randomized mean preserving transformation into binary data and then apply the solution to minimax risk for the case where random variables are binary valued. This shows that minimax risk is attained by a linear strategy and the the set of binary valued distributions contains a least favorable prior. We apply these results to statistics. All unbiased symmetric non-randomized estimates for a function of the mean of a single sample are presented. We find a most powerful unbiased test for the mean of a single sample. We present tight lower bounds on size, type II error and minimal accuracy in terms of expected length of confidence intervals for a single mean and for the difference between two means. We show how to transform the randomized tests that attain the lower bounds into non-randomized tests that have at most twice the type I and II errors. Relative parameter efficiency can be measured in finite samples, in an example on anti-selfdealing indices relative (parameter) efficiency is 60% as compared to the tight lower bound. Our method can be used to generate distribution-free nonparametric estimates and tests when variance is the only parameter of interest. In particular we present a uniformly consistent estimator of standard deviation together with an upper bound on expected quadratic loss. We use our estimate to measure income inequality. en
dc.format.extent 405978 bytes
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher European University Institute
dc.relation.ispartofseries EUI ECO en
dc.relation.ispartofseries 2007/04 en
dc.subject Exact en
dc.subject Distribution-free en
dc.subject Nonparametric inference en
dc.subject Finite sample theory en
dc.subject C14 en
dc.subject C13 en
dc.subject C12 en
dc.subject C44 en
dc.title How to Attain Minimax Risk with Applications to Distribution-Free Nonparametric Estimation and Testing en
dc.type Working Paper en
dc.neeo.contributor SCHLAG|Karl H.|aut|
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