Selection of Fixed Effects in High-dimensional Generalized Linear Mixed Models

The selection of fixed effects is studied in high-dimensional generalized linear mixed models(HDGLMMs) without parametric distributional assumptions except for some moment conditions.The iterative-proxy-based penalized quasi-likelihood method(IPPQL) is proposed to select the important fixed effects where an iterative proxy matrix of the covariance matrix of the random effects is constructed and the penalized quasi-likelihood is adapted.We establish the model selection consistency with oracle properties even for dimensionality of non-polynomial(NP) order of sample size.Simulation studies show that the proposed procedure works well.Besides,a real data is also analyzed.