Abstract:

Inference after model selection is a fundamental problem in high dimensional settings. In the first part of this talk, I will give a selective overview of post-selection inference in statistical and economic fields and discuss why statistical inference after model selection is challenging and. In the second part of this talk, we will focus on a specific topic of post-selection inference. To be specific, we will try to deal with the problem where covariates are generated through high dimensional regularization. It turns out that the regularization step has a very serious effect for valid inference on parameters of interest. Our primary interest is to develop a novel regularized approach to generate covariates. The proposed estimator can be shown to be asymptotically normal. To illustrate, we provide several examples to demonstrate the superiority of the proposed approach. This approach is also applicable to linear or nonlinear functionals in other sparse nonparametric high dimensional regression models such as additive or varying coefficient models.