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MAXIMAL UNIFORM CONVERGENCE RATES INPARAMETRIC 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 problemswith independent, identically nonregularlydistributed data. It focuses on rate efficiency, inthe sense of maximal possible convergence rates ofstochastically bounded estimators, as an optimalitycriterion, largely unexplored in parametricestimation. Under mild conditions, the Hellingermetric, defined on the space of parametricprobability measures, is shown to be an essentiallyuniversally applicable tool to determine maximalpossible convergence rates. These rates are shown tobe attainable in general classes of parametricestimation problems.

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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, RichardBlundell, Andrew Chesher, David Donoho, HideIchimura, Oliver Linton, and two anonymousreferees for helpful comments and discussions.

References

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