Showing papers by "Runze Li published in 2002"

Variable Selection for Cox's proportional Hazards Model and Frailty Model

Abstract: A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave penalized likelihood approach is extended further to the Cox proportional hazards model and the Cox proportional hazards frailty model, two commonly used semi-parametric models in survival analysis. As a result, new variable selection procedures for these two commonly-used models are proposed. It is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function. Further, with a proper choice of the regularization parameter and the penalty function, the proposed estimators possess an oracle property. Standard error formulae are derived and their accuracies are empirically tested. Simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection, and they reduce model complexity as effectively as the best subset variable selection. Compared with the LASSO, which is the penalized likelihood method with the $L_1$ -penalty, proposed by Tibshirani, the newly proposed approaches have better theoretic properties and finite sample performance.

Model selection for analysis of uniform design and computer experiment

Abstract: In this paper, a new variable selection procedure is introduced for the analysis of uniform design and computer experiment. The new procedure is distinguished from the traditional ones in such a way that it deletes insignificant variables and estimates the coefficients of significant variables simultaneously. The new procedure has an oracle property (Fan and Li8). It is better than the best subset variable selection in terms of computational cost and model stability. It is superior to the stepwise regression because it does not ignore stochastic errors during the course of selecting variables. The proposed procedure is illustrated by two examples, one is a typical example of uniform design, and the other one is a classical example for computer experiment.

A Connection Between Variable Selection and EM-Type Algorithms

Abstract: Variable selection is fundamental to high-dimensional statistical modeling. Fan and Li (2001) proposed a class of variable selection procedures via nonconcave penalized likelihood. Optimizing the penalized likelihood function is challenging as it is a highdimensional nonconcave function with singularities. A new algorithm is proposed for finding a solution of the nonconcave penalized likelihood via a modified local quadratic approximation. The proposed algorithm repairs the drawback of Fan and Li’s algorithm. We establish a connection between local quadratic approximation and the so-called MM algorithms, useful extensions of the EM algorithms. This connection enables us to analyze the local and global convergence of the local quadratic approximation algorithm by employing the techniques used for EM algorithms. Moreover, this connection provides a general scheme for constructing a minorizing function in the MM algorithm via the local quadratic approximation.