A Significance Test for Graph-Constrained Estimation

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sen Zhao* and Ali Shojaie
• Companies: University of Washington and University of Washington
• Keywords: Biological networks ; Graph-constrained estimation ; High-dimensional data ; Significance test ; Variable selection

Abstract

Graph-constrained estimation and variable selection methods encourage similarities among neighboring covariates presented as nodes on a graph, and can result in more accurate estimations. However, existing procedures do not provide measures of uncertainty of estimates. Also, most existing approaches assume the incorporated graph information is accurate; violating this assumption could hurt the reliability of the methods. In this paper, we present an inference framework, called the Grace test, which simultaneously produces coefficient estimates and corresponding p-values while incorporating the external graph information. We show that the Grace test asymptotically controls the type-I error rate regardless of the choice of the graph. However, the power of the Grace test depends on the informativeness of the underlying graph. We further propose a more general Grace-ridge test that results in a higher power when the choice of the graph is not fully informative. Our numerical studies show that as long as the graph is reasonably informative, the proposed testing methods deliver improved statistical power over existing inference procedures that ignore external information.?