The Study Of The False Discovery Rate For The Generalized Linear Model

The generalized linear model was proposed by Nelder and Wedderburn in 1972.It is very important cause that it relax the condition of the linear model which requires the response to follow a Gaussian distribution.As a result,it is widely used in practice.The generalized linear model extends the distribution of the response to the exponential family and it can handle the regression problem where the response is discrete or continuous.So the generalized linear model has great value for the attribute data and the count data in biology and medicine.At the same time,with the rapid development of science and technology,the data is becoming more and more complex and its dimension is growing higher and higher.As a result,how to obtain valuable information from data effectively is important.And variable selection get adequate development as a significant method of statistical modelling.Based on the wide application of the generalized linear model and the importance of vari-able selection,this dissertation studies the FDR control of the multiple tests of the regression parameter of the generalized linear model,which is essentially the same as the FDR control of the variable selection.The target is to select variables without including too many false posi-tive variables.And inspired by the knockoff method of Barber and Candes(2015),we proposed the GLM-knockoff method.The main idea of the GLM-knockoff is to construct an knockoff variable as control of the original variable by mimicing the correlation structure of the exist-ing variables,and then control the FDR of the variable selection.In this dissertation,we first prove the GLM-knockoff method can control FDR the low-dimensional generalized linear mod-el.Second,we propose a two-step method to control the FDR of the high-dimensional gener-alized linear model,that is,we first reduce the dimension of the model to low-dimension,then we apply the proposed method to control the FDR and conduct variable selection.Finally,we confirm the effectiveness of our method through simulation study and real data analysis.