An Adaptive Composite Quantile Approach to Dimension Reduction for censored data

Efang Kong (University of Kent)
Wednesday, November 5, 2014 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Sufficient dimension reduction [Li (1991)] has long been a prominent issue in multivariate nonparametric regression analysis. In this paper, we study dimension reduction (DR) for censored data, where semi-parametric structures are assumed for both the dependent variable and the censoring variable. Incorporating the idea of "redistribution-of-mass'' (Efron, 1967; Portnoy, 2003) for dealing with random censoring, we propose an adaptive composite quantile approach. As a general dimension reduction method, it requires minimal assumptions and is capable of recovering the entire DR spaces for both the dependent variable and the censoring variable, and based on numerical evidence is more efficient than some existing methods. Compared withparametric methods such as the Cox proportional hazard (PH) model and the accelerated failure time (AFT) model, our new approach runs less risk of mode misspecification, but retains comparable efficiency due to its use of a structure-adaptive kernel function. Asymptotic results are proved and numerical examples are provided. An application of the new method in the study of the popular primary biliary cirrhosis data, leads to a conclusion more consistent with empirical medical evidence than existing statistical analysis did.