  I propose two U-statistics to test coefficients in generalized linear models.
One of them is used to deal with global hypothesis and the other one to test
with the nuisance parameter. Both the statistics proposed are within
high-dimensional setting which means the number of coefficients is much larger
than the sample size. The statistics are based on quasi-likelihood function so
that they have wilder applications. I theoretically analyze the asymptotic
distribution of the statistics under the null hypothesis and the power
functions under the local and fixed alternatives. To serve as a comparison, the
power functions of the test proposed by Goeman et al. (2011) are also derived.
Some simulation studies are carried out and I apply my methods to an empirical
study.
