Sliced Average Variance Estimation for Censored Data

Abstract

We consider a nonlinear censored regression problem with a vector of predictors. With censoring, high-dimensional regression analysis becomes much more complicated. Since censoring can cause severe bias in estimation, modification to adjust such bias is needed to be made. Based on the weight adjustment, we develop the modification of sliced average variance estimation for estimating the lifetime central subspace without requiring a prespecified parametric model. Our proposed method preserves as much regression information as possible. Simulation results are reported and comparisons are made with the sliced inverse regression of Li et al. (1999).

Keywords:

• Censored regression
• Dimension reduction
• Sliced average variance estimation
• Sliced inverse regression
• Survival analysis
• Visualization

Mathematics Subject Classification:

• Primary 62N01
• Secondary 62G08, 62H05

Acknowledgment

We are grateful to the Editor and two referees for helpful suggestions. We thank Dr. Chun-houh Chen for providing the program of modified SIR.