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Adaptive Non-Parametric Instrumental Regression in the Presence of Dependence

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  • Nicolas ASIN
  • Jan JOHANNES

Abstract

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an independent and identically distributed (iid.) sample it has been shown in Johannes, J. and M. Schwarz [2011] that a least squares estimator based on dimension reduction and thresholding can attain minimax-optimal rates of convergence up to a constant. As this estimation procedure requires an optimal choice of a dimension parameter with regard amongst others to certain characteristics of the unknown structural function we investigate its fully data-driven choice based on a combination of model selection and Lepski's method inspired by Goldenshluger, A. and O. Lepski [2011]. For the resulting fully data-driven thresholded least squares estimator a non-asymptotic oracle risk bound is derived by considering either an iid. sample or by dismissing the independence assumption. In both cases the derived risk bounds coincide up to a constant assuming sufficiently weak dependence characterised by a fast decay of the mixing coefficients. Employing the risk bounds the minimax optimality up to constant of the estimator is established over a variety of classes of structural functions.

Suggested Citation

  • Nicolas ASIN & Jan JOHANNES, 2017. "Adaptive Non-Parametric Instrumental Regression in the Presence of Dependence," Annals of Economics and Statistics, GENES, issue 128, pages 5-66.
  • Handle: RePEc:adr:anecst:y:2017:i:128:p:5-66
    DOI: 10.15609/annaeconstat2009.128.0005
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    More about this item

    Keywords

    Non-Parametric Regression; Instrumental Variable; Dependence; Mixing; Minimax Theory; Adaptive.;

    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
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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