This paper is concerned with selecting important covariates and estimating the index direction simultaneously for high dimensional single-index models. We develop an efficient Threshold Gradient Directed Regularization method via maximizing Distance Covariance (DC-TGDR) between the single index...

In this article, we study a nonparametric approach regarding a general nonlinear reduced form equation to achieve a better approximation of the optimal instrument. Accordingly, we propose the nonparametric additive instrumental variable estimator (NAIVE) with the adaptive group Lasso.We...