On Rate Optimality For Ill-Posed Inverse Problems In Econometrics
AbstractIn 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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 27 (2011)
Issue (Month): 03 (June)
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Other versions of this item:
- Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation for Research in Economics, Yale University.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
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