Simultaneous Confidence Intervals For Multiple Population Comparisons

In the research of practical problems,great capacity of data usually have many characters' parameters,which need to satisfy the specified conditions simultaneously.So simultaneous interval estimations and multiple comparisons become more and more important.Log-normal and binomial distributions are common in biological and medical data.In this paper,simultaneous confidence intervals and multiple comparisons for several means of the two distributions are studied mainly.In chapter 2,a computational test(CAT)based on likelihood ratio and a simultaneous likelihood confidence interval based on CAT are proposed to the pairwise multiple comparison among expected values of log-normal variables.Then they are compared with corresponding generalized variables(GV)methods through two Monte-Carlo simulations and a medical example.The results show that the size and power of CAT are performed better than those of generalized variable test in multiple comparisons,and the simultaneous likelihood confidence interval based on CAT has the smallest volume and the most robust property.In chapter 3,simultaneous confidence intervals for pairwise risk differences of several binomial distributions are constructed.Firstly,the fiducial simultaneous confidence interval(FSCI)is extended to the pairwise risk differences due to the good properties of its frequency.Then generalized simultaneous confidence interval(GSCI)is constructed based on variancestabilizing transformation and fiducial inference.In simulation studies,FSCI and GSCI are compared with the exist simultaneous confidence intervals containing Wald method,Add-1 method,method of variance estimates recovery(MOVER)and Newcombe hybrid score(NHS)method.The numerical results show that FSCI and GSCI are comparable in their properties of frequency.