A1853
Title: Semiparametric estimation and inference for single-index models with high-dimensional covariates
Authors: Ruixuan Liu - Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: A new estimation and inference method for high-dimensional single index models is developed. A simple two-stage estimation method based on the average derivative estimator (ADE) is proposed. This ADE comprises weighted score functions of covariates that can easily be estimated under a semiparametric Gaussian copula structure. In the first stage, standard nonparametric estimates for marginal features and a regularized estimator for the precision matrix of the Gaussian copula are used to obtain high-dimensional score estimands. In the second stage, LASSO type thresholding is conducted to obtain sparse estimates of the index vector in single index models. Both steps involve only convex minimization problems. The rate of convergence of the estimator is derived. Moreover, for inference, asymptotic normality of a de-biased estimator using the one-step Newton-Raphson update is proved.
