On Rate Optimality for Ill-posed Inverse Problems in Econometrics
Xiaohong Chen () and
Markus Reiss ()
No 1626, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University
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 the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases. 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.
Keywords: Nonparametric instrumental regression; Nonparametric indirect regression; Statistical ill-posed inverse problems; Minimax risk lower bound; Optimal rate (search for similar items in EconPapers)
JEL-codes: C14 C30 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9) Track citations by RSS feed
Published in Econometric Theory (2011), 27(3): 497-521
Downloads: (external link)
Journal Article: ON RATE OPTIMALITY FOR ILL-POSED INVERSE PROBLEMS IN ECONOMETRICS (2011)
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:cwl:cwldpp:1626
Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.
Access Statistics for this paper
More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Matthew Regan ().