Confidence Intervals in Two Variance Components Mixed Model

In the two variance components mixed model, Y = Xβ + ZA + e , where Y(nx1) is a random vector, X(nxp) is a known matrix with rank p, β = ( β₁, β₂, ..., β_p ) , β₁, β₂, ..., β_p are unknown parameters. A and e are mutually independent normal random vectors with zero means, Z is known matrix. The confidence intervals for variance σ²_A by using Tukey-Williams method s is given by Ofversten (1993). This article shows that the probability ranges of confidence intervals for σ²_A are equals and whether greater than 1- α or not in the two variance components mixed model.