arXiv 12 Nov 2015 · Statistics — Computation · publishedElectronic Journal of Statistics (2021) · 6 citations (OpenAlex)
arXiv:1511.03977 · PDF · DOI · OpenAlex · Extracted main text
The problem of endogeneity in statistics and econometrics is often handled by introducing instrumental variables (IV) which fulfill the mean independence assumption, i.e. the unobservable is mean independent of the instruments. When full independence of IV's and the unobservable is assumed, nonparametric IV regression models and nonparametric demand models lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates for the mean integrated square error of the iteratively regularized Newton method applied to these problems. Compared to related results we derive stronger convergence results that rely on weaker nonlinearity restrictions. We demonstrate in numerical simulations for a nonparametric IV regression that the method produces better results than the standard model.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Dunker, F., Florens, J.-P., Hohage, T., Johannes, J., and Mammen, E (2014) Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression self | 1.000 | 6 | 3 | 100% |
| 2 | Horowitz, J. L. and Lee, S (2007) Nonparametric instrumental variables estimation of a quantile regression model | 0.874 | 13 | 2 | 100% |
| 3 | Bauer, F., Hohage, T., and Munk, A (2009) Iteratively regularized gauss–newton method for nonlinear inverse problems with random noise | 0.737 | 4 | 3 | 50% |
| 4 | Chen, X. and Reiss, M (2011) On rate optimality for ill-posed inverse problems in econometrics | 0.644 | 2 | 2 | 100% |
| 5 | Chen, X. and Christensen, T. M (2015) Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation | 0.644 | 2 | 2 | 100% |
| 6 | Hall, P. and Horowitz, J. L (2005) Nonparametric methods for inference in the presence of instrumental variables | 0.644 | 2 | 2 | 100% |
| 7 | Bakushinski, A. B. and Kokurin, M (2004) Iterative Methods for Approximate Solution of Inverse Problems | 0.511 | 2 | 2 | 50% |
| 8 | Bakushinski, A. B (1992) On a convergence problem of the iterative-regularized Gauss-Newton method | 0.511 | 2 | 2 | 50% |
| 9 | Mathé, P (2006) The lepskii principle revisited | 0.511 | 2 | 2 | 50% |
| 10 | McDiarmid, C (1989) On the method of bounded differences | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 56 scored citations.