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On Rate Optimality for Ill-posed Inverse Problems in Econometrics

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Author Info
Xiaohong Chen () (Cowles Foundation, Yale University)
Markus Reiss (University of Heidelberg)
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.

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File URL: http://cowles.econ.yale.edu/P/cd/d16a/d1626.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1626.

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Length: 27 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:cwl:cwldpp:1626

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Nonparametric instrumental regression; Nonparametric indirect regression; Statistical ill-posed inverse problems; Minimax risk lower bound; Optimal rate;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Darolles, S. & Florens, J.-P. & Renault, É., 2002. "Nonparametric Instrumental Regression," Cahiers de recherche 05-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  2. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, 07. [Downloadable!] (restricted)
    Other versions:
  3. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01. [Downloadable!] (restricted)
  4. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July. [Downloadable!] (restricted)
  5. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  6. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, SŽbastien, 2007. "Identification and estimation by penalization in nonparametric instrumental regression," CORE Discussion Papers 2007085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  7. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November. [Downloadable!] (restricted)
  8. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier. [Downloadable!] (restricted)
  9. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November. [Downloadable!] (restricted)
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