Tests for high dimensional generalized linear models

We consider testing regression coefficients in high dimensional generalized linear models. By modifying the test statistic of Goeman and his colleagues for large but fixed dimensional settings, we propose a new test, based on an asymptotic analysis, that is applicable for diverging dimensions and is robust to accommodate a wide range of link functions. The power properties of the tests are evaluated asymptotically under two families of alternative hypotheses. In addition, a test in the presence of nuisance parameters is also proposed. The tests can provide p-values for testing significance of multiple gene sets, whose application is demonstrated in a case-study on lung cancer.National Science Foundation [DSM-1309210]; China's National Natural Science Foundation [11131002, 71371016]; National Key Basic Research Program [2015CB856000]; Center for Statistical Science and Laboratory of Mathematical Economics and Quantity Finance at Peking UniversitySCI(E)ARTICLEcsx@gsm.pku.edu.cn51079-11027