ON RATE OPTIMALITY FOR ILL-POSED INVERSE PROBLEMS IN ECONOMETRICS
Xiaohong Chen () and
Markus Reiss ()
Econometric Theory, 2011, vol. 27, issue 3, 497-521
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.
References: Add references at CitEc
Citations: View citations in EconPapers (40) Track citations by RSS feed
Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)
Working Paper: On Rate Optimality for Ill-posed Inverse Problems in Econometrics (2007)
Working Paper: On rate optimality for ill-posed inverse problems in econometrics (2007)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:27:y:2011:i:03:p:497-521_00
Access Statistics for this article
More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Keith Waters ().