Likelihood Ratio Test For High Dimensional Covariates

Many popular methods in the model selection have been successfully used in high dimensional hypothesis testing, which has become a hypotheses test analysis method. In particular, Fan and Peng (2004) firstly applied the likelihood ratio test to the penalized likelihood context. They demonstrated that under some regularity conditions, the classical likelihood theory continues to hold for p=o(n1/5). In our thesis, we want to remove the restriction p=o(1/5). We first select the model s by the LASSO, SCAD or MCP, then add the variables s1, which are the variables that we want to test, to the model s. Finally, in the new model s U s1, we use the classical likelihood ratio test method to test variables S1. Our numerical studies also show that the proposed approach has satisfactory performance.