APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

3.6. Simultaneous Confidence Intervals

If H₀: LB = 0 is rejected, it may be of interest to provide the confidence intervals for the individual components of LB (or B if L= I_k+1) or the linear functions of these components. Under the assumption of the full rank of X, a set of simultaneous confidence intervals for the linear combinations of the type c′LBd corresponding to the linear hypothesis H₀: LB = 0 can be constructed.

Noting that H₀^(c,d) : (c′LBd=0 is true for all c and d if and only if H₀ is true, we can write H₀ as the intersection of all such H₀^(c,d) : (c′LBd=0. Testing of H₀^(c,d) : c′LBd=0 can be done using the appropriate F test. Let the corresponding F statistic be F^(c,d) and let F_α be the cutoff point. Then, H₀ is not rejected if ...