Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression

作者：Dunker Fabian^*; Florens Jean Pierre; Hohage Thorsten; Johannes Jan; Mammen Enno

来源：Journal of Econometrics, 2014, 178: 444-455.

DOI：10.1016/j.jeconom.2013.06.001

• Nonparametric regression
• Nonlinear inverse problems
• Iterative regularization
• Instrumental regression

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.

• 出版日期2014-1