High Dimensional Tests Based on U-Statistics for Generalized Linear Models

Abstract

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.