Sliced Inverse Regression

Sliced Inverse Regression (SIR) proposed by Ker-Chau Li (1991) is a widely used semiparametric technique to reduce the dimensions of regression problems.

Two papers based on the concept of SIR and its generalization have been submitted, for forecasting macroeconomic series and statistical process monitoring.

- Cluster-Based Regularized Sliced Inverse Regression for Forecasting Macroeconomic Variables

- Abstract: This article concerns the dimension reduction in regression for large dataset. We introduce a new method based on the sliced inverse regression approach, called cluster-based regularized sliced inverse regression. Our method not only keeps the merit of considering both response and predictors information, but also enhances the capability of handling highly correlated variables. It is justified under certain linearity conditions. An empirical application on macroeconomic dataset shows that our method outperformed the dynamic factor model and other shrinkage methods.

My seminar talk in UIC: Slides

- Partial Sliced Inverse Regression for Quality-Relevant Multivariate Statistical Process Monitoring

- Abstract: The concept of the quality-relevant multivariate statistical process monitoring is to monitor the abnormal observations in the measurements. This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into this area. Provides an extension of SIR for the single-index model by adopting the idea from partial least squares (PLS). Our partial sliced inverse regression (PSIR) method has the merit of incorporating information from both predictors (X) and responses (Y), and it has capability of handling large, nonlinear, or “n<p” dataset. Two statistics with their corresponding distributions and control limits are given based on the X-space decomposition of PSIR for the purpose of fault detection in process monitoring. Simulations showed PSIR outperformed over PLS and SIR for both linear and nonlinear model.