In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to derive (xx see paper).

IV regression in the context of a re-sampling is considered in the work. Comparatively, the contribution in the development is a structural identication in the IV model. The work also contains a multiplier-bootstrap justication.

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...