Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g, is discontinuous and must be regularized to permit consistent estimation. The optimal regularization parameter depends on population characteristics that are unknown in applications. This paper presents a theoretically justified empirical method for choosing the regularization parameter in series estimation. The method adapts to the unknown smoothness of g and other unknown functions. The resulting estimator of g converges at least as fast as the optimal rate multiplied by (logn)1/2. The asymptotic integrated mean-square error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE.