Partial Consistency with Sparse Incidental Parameters.

ABSTRACT: Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we first apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their consistency and asymptotic normality, which reveals an oracle property. However, the penalized estimators for the incidental parameters possess only partial selection consistency but not consistency. This is an interesting partial consistency phenomenon: the structural parameters are consistently estimated while the

SUBMITTER: Fan J 

PROVIDER: S-EPMC6788862 | biostudies-literature | 2018 May

REPOSITORIES: biostudies-literature