|Title||LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||Shi, Chengchun, Rui Song, Zhao Chen, and Runze Li|
|Date Published||2019 Oct|
This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.
|Alternate Journal||Ann Stat|
|Original Publication||Linear hypothesis testing for high dimensional generalized linear models.|
|PubMed Central ID||PMC6750760|
|Grant List||P01 CA142538 / CA / NCI NIH HHS / United States |
P50 DA036107 / DA / NIDA NIH HHS / United States
P50 DA039838 / DA / NIDA NIH HHS / United States
T32 LM012415 / LM / NLM NIH HHS / United States
LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.