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 ( log n ) 1 / 2 . The asymptotic integrated mean-square error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE.