Valid Simultaneous Confidence Intervals Of Multiple Predictors For Post Model Selection

Multiple comparisons and simultaneous confidence intervals are a kind of problem that consider the statistical properties of multiple parameters simultaneously,It is the essential part in the fields of biomedicine,sociology,economics,clinical trials and so on.The hypothesis testing method for a single parameter is no longer valid on multiple parameters,and the error rate needs to be redefined.In the data analysis research,the traditional approach is to perform model selection before statistical inference,but such statistical inference is not based on the data itself since the process of model selection is random.Statistical inference sometimes is invalid when the priori model selection has been assumed to be correct.This paper considers the case of linear model.We construct the simultaneous confidence intervals for multiple predictors based on the valid confidence interval for the single post-model-selection predictor.This paper use the Bonferroni method and Scheffe method to give the form of the simultaneous confidence interval which is post model selection,and present the calculation method of the quantile.The coverage rate and corresponding interval length were calculated numerically by using the Monte Carlo simulation,and the coverage effects of simultaneous confidence intervals constructed by different methods are compared.The conclusions and methods in this paper enrich the theory and algorithms of the multiple comparisons which is post model selection,and this will help solve problems in application areas such as clinical trials and biostatistics.