| Traditional statistical inference is based on the specified model,which may lead to the risk of misjudgment,so statisticians propose selective inference.As a classical way of data processing,data splitting divides data into two parts,one for model selection and the other for inference,which easily solves the problems of selective inference,but it does not have a high utilization of data.In this dissertation,we use the data carving to process the data in the selective inference.It divides the sample data into two parts,one part of the data is used for model selection,and the other part is used for selective inference together with the data of the selected model.Compared with the data splitting,this method improves the utilization of the data.For the selected model,parameter inference is performed by controlling the selective type I error rate.Linear regression model has simple structure and strong interpretability,but its response variables need to follow normal distribution,which has limitations.In fact,we will encounter lots of non-normal or even non-continuous data,so this dissertation extends some work of selective inference of linear regression model to the situation of generalized linear model,and uses the data carving to process the sample data,so as to improve the practicability of selective inference.In research fields such as bioinformatics and financial engineering,the variance of data is usually unknown,and it is difficult to estimate the variance of such high-dimensional data.On the other hand,based on the generalized linear model,this dissertation uses lasso and square root lasso to infer the model selectively,and compares them.It is worth noting that the optimization parameters of square root lasso are not affected by the noise fluctuation in the data,and its calculation is more convenient than lasso,and its application scope is wider.When the data follows any exponential family distribution,the uniform most power unbiased selective test of the parameters of interest is obtained,and the selective confidence intervals are obtained by the selective test.The simulation results show that the interval coverage is improved and the selective confidence interval is shortened. |
