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MAXIMAL UNIFORM CONVERGENCE RATES IN PARAMETRIC ESTIMATION PROBLEMS

Published online by Cambridge University Press:  18 August 2009

Walter Beckert  and
Daniel L. McFadden
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Abstract

This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 469 - 500
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

We are indebted to Masafumi Akahira, Richard Blundell, Andrew Chesher, David Donoho, Hide Ichimura, Oliver Linton, and two anonymous referees for helpful comments and discussions.

References

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