A Significance Test for Graph-Constrained Estimation #MMPMID26393533
Zhao S; Shojaie A
Biometrics 2016[Jun]; 72 (2): 484-93 PMID26393533show ga
Graph-constrained estimation methods encourage similarities among neighboring covariates presented as nodes of a graph, and can result in more accurate estimates, especially in high-dimensional settings. Variable selection approaches can then be utilized to select a subset of variables that are associated with the response. However, existing procedures do not provide measures of uncertainty of the estimates. Further, the vast majority of existing approaches assume that available graph accurately captures the association among covariates; violations to this assumption could severely hurt the reliability of the resulting estimates. In this paper, we present a new inference framework, called the Grace test, which produces coefficient estimates and corresponding p-values by incorporating the external graph information. We show, both theoretically and via numerical studies, that the proposed method asymptotically controls the type-I error rate regardless of the choice of the graph. We also show that when the underlying graph is informative, the Grace test is asymptotically more powerful than similar tests that ignore the external information. We study the power properties of the proposed test when the graph is not fully informative and develop a more powerful Grace-ridge test for such settings. Our numerical studies show that as long as the graph is reasonably informative, the proposed inference procedures deliver improved statistical power over existing methods that ignore external information.
free
free
free
Biometrics 2016 ; 72 (2): 484-93
