Working paper
Iterative Regularization in Nonparametric Instrumental Regression
Jan Johannes, Sébastien Van Bellegem, and Anne Vanhems
IDEI Working Paper
n. 630, July 2010
Reference
Jan Johannes, Sébastien Van Bellegem, and Anne Vanhems, “Iterative Regularization in Nonparametric Instrumental Regression”, IDEI Working Paper, n. 630, July 2010.
Abstract
We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an illposed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.
Keywords
Nonparametric estimation; Instrumental variable; Ill-posed inverse problem;
JEL codes
- C14: Semiparametric and Nonparametric Methods: General
- C30: General