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Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence

Author

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  • Fabian Dunker

    (Georg-August-University Göttingen)

Abstract

In econometrics some nonparametric instrumental regression models and nonparametric demand models with endogeneity lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates of the risk for the iteratively regularized Newton method applied to these problems. Compared to related results we relay on a weaker non-linearity condition and have stronger convergence results. We demonstrate by numerical simulations for a nonparametric IV regression problem with continuous instrument and regressor that the method produces better results than the standard method.

Suggested Citation

  • Fabian Dunker, 2015. "Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 192, Courant Research Centre PEG.
    • Handle: RePEc:got:gotcrc:192
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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_192.pdf
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    More about this item

    Keywords

    Nonparametric regression; instrumental variables; nonlinear inverse problems; iterative regularization;
    All these keywords.

    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
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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