Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression
(2014) Journal of Econometrics — Vol. 178, n° 3, p. 444-455 (2014)
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- This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data.
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Dunker, F., Florens, J.-P., Hohage, T., Johannes, J., & Mammen, E. (2014). Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression. Journal of Econometrics, 178(3), 444-455. https://doi.org/10.1016/j.jeconom.2013.06.001 (Original work published 2014)