A Robust Approach to SIR Estimation

Jason Bond
Ph.D., 1999
Advisor: Ker-Chau Li
The robustness of the Sliced Inverse Regression (SIR) methodology is studied under conditions where a specific form of contamination is introduced into the co-variate distribution. The concept of effective dimension reduction space (EDR) is discussed as well as are various methods that attempt to estimate spaces of reduced dimension in dependent-independent modeling. The effectiveness of several standard robust covariance estimation methods when used in estimation of the EDR directions are also discussed. Perturbation results are derived for the SIR generalized eigenvalue problem. These results are applied towards a Gibbs sampling algorithm to estimate the EDR directions in the presence of data contamination.