ABSTRACT
In a series of three papers, Wald ( 1940, 1941 , 194 7) proposed a procedure for constructing exact confidence intervals on certain ratios of variance components in unbalanced experimental designs. Seely and El-Bassiouni (1983) generalized this approach and derived conditions under which the method can be applied. Harville and Fenech (1985) considered computational aspects of the problem and also derived approximate intervals that are simple to compute. Using the notation of Harville and Fenech, consider the mixed model with one set of random effects (in addition to the set of residual effects)
r = X~ + Z§. + !i (B.l) where r is anN X 1 vector of observations, ~is a p X 1 vector of unknown parameters, §. and g_ are m x 1 and N x 1 independent multivariate normal random vectors with mean vector 0 and variancecovariance matrices cr1Im and cr~IN, respectively, and-Im and IN are identity matrices of order m and N, respectively. The matrices X and Z are of dimensions N X p and N x m, respectively, and represent design matrices for the fixed and random effects. Finally, define p* =
