Runze Li

TL;DR: This paper proposes a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood, and investigates the asymptotic behavior of the proposed test and demonstrates its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters.

TL;DR: This proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches, and shows that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001).

TL;DR: A novel, sufficient optimality condition that relies on a convex differencing representation of the penalized loss function and the subdifferential calculus is introduced that enables the oracle property for sparse quantile regression in the ultra-high dimension under relaxed conditions.

TL;DR: This work proposes adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and proves that the methods possess the oracle property.

TL;DR: In this article, a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed, and a kernel estimator is developed.