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Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation

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    This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h_0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h_0 and its derivatives when h_0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L^2-norm rates for severely ill-posed problems, and are only up to a [log(n)]^epsilon (with epsilon

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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1923-r.pdf
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    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1923R.

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    Length: 36 pages
    Date of creation: Nov 2013
    Date of revision: Apr 2015
    Handle: RePEc:cwl:cwldpp:1923r
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    Yale University, Box 208281, New Haven, CT 06520-8281 USA

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    Fax: (203) 432-6167
    Web page: http://cowles.yale.edu/

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

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