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ON RATE OPTIMALITY FOR ILL-POSED INVERSE PROBLEMS IN ECONOMETRICS

Published online by Cambridge University Press:  11 October 2010

Xiaohong Chen  and
Markus Reiss
Xiaohong Chen*
Affiliation:
Yale University
Markus Reiss
Affiliation:
Humboldt University Berlin
*
*Address correspondence to Xiaohong Chen, Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520 USA; e-mail: [email protected].
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Abstract

In this paper we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and NPIV models under two basic regularity conditions: the approximation number and the link condition. We show that both a simple projection estimator for the NPIR model and a sieve minimum distance estimator for the NPIV model can achieve the minimax risk lower bounds and are rate optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 3: SPECIAL ISSUE ON INVERSE PROBLEMS IN ECONOMETRICS , June 2011 , pp. 497 - 521
Copyright
Copyright © Cambridge University Press 2011

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References

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