TY - JOUR
T1 - A regularization-based adaptive test for high-dimensional generalized linear models
AU - Wu, Chong
AU - Xu, Gongjun
AU - Shen, Xiaotong
AU - Pan, Wei
N1 - Publisher Copyright:
© 2020 Chong Wu, Gongjun Xu, Xiaotong Shen and Wei Pan.
PY - 2020/6
Y1 - 2020/6
N2 - In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer's Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer's disease. We also put R package \aispu"implementing the proposed test on GitHub.
AB - In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer's Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer's disease. We also put R package \aispu"implementing the proposed test on GitHub.
KW - Adaptive Test
KW - Gene-Environmental Interaction
KW - Truncated Lasso Penalty
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M3 - Article
AN - SCOPUS:85094909789
SN - 1532-4435
VL - 21
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
ER -