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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

Suggested Citation

  • Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation," Cowles Foundation Discussion Papers 1923R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
  • Handle: RePEc:cwl:cwldpp:1923r
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    Citations

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    Cited by:

    1. Michael Jansson & Demian Pouzo, 2017. "Some Large Sample Results for the Method of Regularized Estimators," Papers 1712.07248, arXiv.org.
    2. Demian Pouzo, 2015. "On the Non-Asymptotic Properties of Regularized M-estimators," Papers 1512.06290, arXiv.org, revised Oct 2016.
    3. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Babii, Andrii & Florens, Jean-Pierre, 2017. "Distribution of residuals in the nonparametric IV model with application to separability testing," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    5. Babii, Andrii, 2017. "Honest confidence sets in nonparametric IV regression and other ill-posed models," TSE Working Papers 17-803, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Ill-posed inverse problems; Series 2SLS; Optimal sup-norm convergence rates; Adaptive estimation; Random matrices; Bootstrap uniform confidence bands; Nonlinear welfare functionals; Nonparametric demand analysis with endogeneity;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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