Sufficient Dimension Reduction and Variable Selection for Large-p-Small-n Data With Highly Correlated Predictors

Sufficient dimension reduction (SDR) is a paradigm for reducing the dimension of the predictors without losing regression information. Most SDR methods require inverting the covariance matrix of the predictors. This hinders their use in the analysis of contemporary datasets where the number of predictors exceeds the available sample size and the predictors are highly correlated. To this end, by incorporating the seeded SDR idea and the sequential dimension-reduction framework, we propose a SDR method for high-dimensional data with correlated predictors. The performance of the proposed method is studied via extensive simulations. To demonstrate its use, an application to microarray gene expression data where the response is the production rate of riboflavin (vitamin B₂) is presented.