If H_{0}: 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 H_{0}: LB = 0 can be constructed.

Noting that H_{0}^{(c,d)} : (c′LBd=0 is true for all c and d if and only if H_{0} is true, we can write H_{0} as the intersection of all such H_{0}^{(c,d)} : (c′LBd=0. Testing of H_{0}^{(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, H_{0} is not rejected if ...

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