Suppose we have I = 2 groups and the models y1jt = t + 1t + v1jt for the j = 1, . . .

Suppose we have I = 2 groups and the models y1jt = µt + α1t + v1jt for the j = 1, . . . , N observations in group 1 and y2jt = µt + α2t + v2jt for the j = 1, . . . , N observations in group 2, with α1t + α2t = 0. Suppose we want to test equality of the two group means; i.e., yijt = µt + vijt, i = 1, 2.

Derive the residual and error power components corresponding to (7.83) and

(7.84) for this particular case.

Verify the forms of the linear compounds involving the mean given in (7.90)

and (7.91), using (7.88) and (7.89).

Show the ratio of the two smoothed spectra in (7.103) has the indicated Fdistribution when f1(ω) = f2(ω). When the spectra are not equal, show the variable is proportional to an F-distribution, where the proportionality constant depends on the ratio of the spectra.