  We consider testing regression coefficients in high dimensional generalized
linear models. An investigation of the test of Goeman et al. (2011) is
conducted, which reveals that if the inverse of the link function is unbounded,
the high dimensionality in the covariates can impose adverse impacts on the
power of the test. We propose a test formation which can avoid the adverse
impact of the high dimensionality. When the inverse of the link function is
bounded such as the logistic or probit regression, the proposed test is as good
as Goeman et al. (2011)'s test. The proposed tests provide p-values for testing
significance for gene-sets as demonstrated in a case study on an acute
lymphoblastic leukemia dataset.
