The objectives of this proposal are (1) to enrich the variable selection alternatives by merging ideas from the variable selection and dimension reduction areas, and (2) develop variable screening procedures using alternative methods of association learning. The specific goals include: a) develop post-dimension reduction model checking procedures, b) develop variable selection procedures using the model checking procedures and multiple testing ideas, c) develop dimension reduction procedures for very high dimensional data using matrix regularization, d) develop variable screening based on partial correlation learning, e) develop variable screening using nonparametric association learning.
In many areas of contemporary research, including gene expression and proteomics studies, biomedical imaging, functional magnetic resonance imaging, tomography, tumor classifications, signal processing, image analysis, finance, text retrieval and climate studies, the data collected include a large number of variables with only a few of them being relevant for prediction. Procedures for identifying the relevant predictors have mostly been developed under certain model assumptions and may fail to discern the relevance of some important predictors. The proposed research aims at developing variable screening and variable selection procedures which do not rely on potentially restrictive modeling assumptions.
