Penalized Independence Rule for Testing High-Dimensional Hypotheses

Abstract

We consider a challenging problem of testing any possible association between a response variable and a set of predictors, when the dimensionality of predictors is much greater than the number of observations. In the context of generalized linear models, a new approach is proposed for testing against high-dimensional alternatives. Our method uses soft-thresholding to suppress stochastic noise and applies the independence rule to borrow strength across the predictors. Moreover, the method can provide a ranked predictor list and automatically select “important” features to retain in the test statistic. We compare the performance of this method with some competing approaches via real data and simulation studies, demonstrating that our method maintains relatively higher power against a wide family of alternatives.

Keywords:

• High-dimensional data
• Hypothesis testing
• Independence rule
• Power
• Soft-thresholding

Mathematics Subject Classification:

• 62F03
• 62J07

Acknowledgments

This research was partially supported by the National High Technology Research and Development Program of China (2006AA10A102) and the National Basic Research Program (973) of China (2008CB117002). The authors thank the reviewer for helpful comments.