Are Super-efficient Estimators Super-powerful?

We consider inference problems in two parametric families where estimators which are super-efficient relative to the maximum likelihood estimator (mle) exist. We examine whether tests based on these super-efficient estimators perform better than the tests based on the mle's. The measures of tes...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2004-12, Vol.33 (9), p.2003-2013
Main Author: Sethuraman, Jayaram
Format: Article
Language:English
Subjects:
Exact sciences and technology
General topics
Mathematics
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:We consider inference problems in two parametric families where estimators which are super-efficient relative to the maximum likelihood estimator (mle) exist. We examine whether tests based on these super-efficient estimators perform better than the tests based on the mle's. The measures of test efficiency used are Pitman efficiency, Bayes risk efficiency, Bahadur and Hodges-Lehmann efficiencies.
ISSN:0361-0926
1532-415X
DOI:10.1081/STA-200026561