Exact Tests of Variance Components in Nested Error Component Regression Model

In this paper, some new exact tests and confidence intervals of variance components in nested error component regression model with three random effects are developed by using generalized p-value and generalized confidence interval. Invariance of these tests and confidence intervals under scale transformation is also discussed. It is showed that the generalized p-value is feasible and effective to resolve the hypothesis testing problems with nuisance parameters. A simulation study is conducted to illustrate the powers of these tests and coverage probabilities.