Interval Estimation Of Variance Components In Unbalanced Heteroscedastic Two-Way Random Effects Model

In this paper,the confidence interval of variance components are studied in unbalanced heteroscedastic two-way random effects model,the paper includes the following two aspects:1.The confidence intervals are studied for variance components of interest in the above model based on the confidence distribution idea.Firstly,we construct the asymptotic confidence distribution and the combined asymptotic confidence distribution of variance components.Then,the confidence interval is derived naturally by the property of confidence distribution.Lastly,a simulation study is conducted to compare the derived confidence interval with the interval based on other methods in terms of both empirical coverage probability and average interval length,results demonstrate that the intervals the confidence distribution performs better in most circumstances.2.The confidence intervals are studied for variance components of interest in the same model based on the fiducial generalized inference idea.Firstly,we construct structure equations of all variance components(include variances of random error)based on their minimal sufficient.Then,the fiducial generalized pivotal quantity is obtained through solving an implicit equation for the parameter of interest,and the confidence interval can be derived naturally.Lastly,a simulation study is conducted to compare the derived confidence interval with the intervals based on confidence distribution and other methods in terms of both empirical coverage probability and average interval length,results demonstrate that fiducial generalized inference and confidence distribution have their own advantages,but they are better than other methods in most circumstances.