On rate optimality for ill-posed inverse problems in econometrics

Xiaohong Chen () and Markus Reiss

No CWP20/07, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 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.

JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2007-09-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (32)

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Related works:
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)
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