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2016 ; 72
(2
): 484-93
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A significance test for graph-constrained estimation
#MMPMID26393533
Zhao S
; Shojaie A
Biometrics
2016[Jun]; 72
(2
): 484-93
PMID26393533
show 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
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 article, 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.
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